BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Alexander Mangerel (CRM\, Montreal)
DTSTART:20200716T170000Z
DTEND:20200716T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/1
DESCRIPTION:Title: Squarefree Integers in Arithmetic Progressions to Smooth/Fria
ble Moduli\nby Alexander Mangerel (CRM\, Montreal) as part of ViBraNT
(Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nI will discuss ho
w to obtain an asymptotic formula (with power-savings error term) for the
count of squarefree integers in an arithmetic progression when the modulus
does not have any large prime factors\, using a blend of cohomological te
chniques and p-adic methods. For this collection of moduli our results go
beyond the best existing admissible range obtained recently by Nunes.\n\nT
his is joint work with C. Perret-Gentil.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jing Zhao (Max Planck)
DTSTART:20200730T170000Z
DTEND:20200730T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/2
DESCRIPTION:Title: Discrete negative moments of $\\zeta'(\\rho)$\nby Jing Zh
ao (Max Planck) as part of ViBraNT (Virtual Brazilian Number Theory semina
r)\n\n\nAbstract\nI shall talk about a recent result of a joint work with
Winston Heap and Junxian Li. We proved lower bounds for the discrete negat
ive 2kth moments of the derivative of the Riemann zeta function\, which ag
rees with a conjecture of Gonek and Hejhal. We also proved a general formu
la for the discrete twisted 2nd moment of the Riemann zeta function. This
agrees with a conjecture of Conrey and Snaith.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramon Nunes (UFC)
DTSTART:20200723T170000Z
DTEND:20200723T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/3
DESCRIPTION:Title: Moments of k-free numbers in arithmetic progressions.\nby
Ramon Nunes (UFC) as part of ViBraNT (Virtual Brazilian Number Theory sem
inar)\n\n\nAbstract\nWe will discuss the moments of distribution of $k$-fr
ee numbers in arithmetic progressions for which we show estimates improvin
g on previous results by Hall and the author. We will present conjectures
due mainly to Montgomery and according to which our results are nearly opt
imal. The key new idea is to complement Hall's argument based on the so-ca
lled fundamental lemma of Montgomery and Vaughan with some elementary esti
mates on the region where the previous approach is wasteful.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Winston Heap (Max Planck)
DTSTART:20200806T170000Z
DTEND:20200806T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/4
DESCRIPTION:Title: Random multiplicative functions and a model for the Riemann z
eta function\nby Winston Heap (Max Planck) as part of ViBraNT (Virtual
Brazilian Number Theory seminar)\n\n\nAbstract\nWe look at a weighted sum
of random multiplicative functions and view this as a model for the Riema
nn zeta function. We investigate various aspects including its high moment
s\, distribution and maxima.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Chirre (NTNU)
DTSTART:20200924T170000Z
DTEND:20200924T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/5
DESCRIPTION:Title: The behavior of the argument of the Riemann zeta-function
\nby Andrés Chirre (NTNU) as part of ViBraNT (Virtual Brazilian Number Th
eory seminar)\n\n\nAbstract\nIn this talk we will review some recent resul
ts related to the argument function of the Riemann zeta function\, assumin
g the Riemann hypothesis. The use of bandlimited approximations and the re
sonance method will help us to describe the behavior of this oscillatory f
unction. Finally\, we will extend these results to the antiderivatives of
the argument function that encode\, in a certain way\, information about t
he argument function.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Chow (Warwick)
DTSTART:20200813T170000Z
DTEND:20200813T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/6
DESCRIPTION:Title: Moments of Weyl sums\, restriction estimates\, and diophantin
e equations\nby Sam Chow (Warwick) as part of ViBraNT (Virtual Brazili
an Number Theory seminar)\n\n\nAbstract\nWe discuss the role played by mom
ent estimates for Weyl sums in counting solutions to diophantine equations
\, and the analogous role played by restriction estimates in the combinato
rial theory of diophantine equations. Additionally\, we sketch some modern
techniques used to prove such estimates.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Klurman (Max Planck and University of Bristol)
DTSTART:20200827T170000Z
DTEND:20200827T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/7
DESCRIPTION:Title: Monotone chains in multiplicative sets\nby Oleksiy Klurma
n (Max Planck and University of Bristol) as part of ViBraNT (Virtual Brazi
lian Number Theory seminar)\n\n\nAbstract\nIt is a rather difficult task t
o show that given a general sequence $a(1)\,a(2)\\dots$ and admissible set
of integers $h_1\,h_2\\dots h_k$ each possible arrangement $a(n+h_1)\\le
a(n+h_2)\\le\\dots a(n+h_k)$ occurs for infinitely many integers $n.$\nIn
this talk\, we describe how recent advances in multiplicative number theor
y and theory of automorphic forms allow us to shed some light on such ques
tions related to the coefficients of Hecke cusp forms\n(based on a joint w
ork with A. Mangerel).\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Harper (Warwick)
DTSTART:20200820T170000Z
DTEND:20200820T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/8
DESCRIPTION:Title: Multiplicative chaos in number theory\nby Adam Harper (Wa
rwick) as part of ViBraNT (Virtual Brazilian Number Theory seminar)\n\n\nA
bstract\nMultiplicative chaos is the general name for a family of probabil
istic objects\, which can be thought of as the random measures obtained by
taking the exponential of correlated Gaussian random variables. Multiplic
ative chaos turns out to be closely connected with various problems in ana
lytic number theory\, including the value distribution of the Riemann zeta
function on the critical line\, the moments of character sums\, and vario
us model versions of these problems. I will try to give a gentle introduct
ion to these issues and connections\, presenting both results and open pro
blems without assuming too much background knowledge. (This will be a ligh
tly updated version of the talk I gave last year in Cetraro.)\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gady Kozma (Weizmann Institute of Science)
DTSTART:20200910T170000Z
DTEND:20200910T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/9
DESCRIPTION:Title: Random polynomials\, sieves and Dedekind zeta functions\n
by Gady Kozma (Weizmann Institute of Science) as part of ViBraNT (Virtual
Brazilian Number Theory seminar)\n\n\nAbstract\nWhat is the probability th
at a random polynomial with coefficients +/-1 is irreducible over the rati
onals? This fascinating problem\, still open\, has seen a lot of progress
in the last few years. We will survey this progress\, with particular emph
asis on new results\, joint with Lior Bary-Soroker and Dimitris Koukoulopo
ulos.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Gerspach (ETH\, Zürich)
DTSTART:20200903T170000Z
DTEND:20200903T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/10
DESCRIPTION:Title: Low pseudomoments of the Riemann zeta function and its power
s\nby Maxim Gerspach (ETH\, Zürich) as part of ViBraNT (Virtual Brazi
lian Number Theory seminar)\n\n\nAbstract\nThe pseudomoments of the Rieman
n zeta function are the moments of the partial sums associated to zeta on
the critical line. Using probabilistic methods of Harper\, we provide boun
ds which imply the order of magnitude of all pseudomoments. We also provid
e upper and lower bounds for the pseudomoments of the powers of zeta that
are almost-matching when combined with previous bounds of Bondarenko\, Hea
p and Seip\, and turn out to behave in a somewhat different manner. In thi
s talk\, I will mostly try to give a heuristic argument in support of the
results by relating these quantities to moments of random multiplicative f
unctions and to random Euler products.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucile Devin (University of Gothenburg)
DTSTART:20201001T170000Z
DTEND:20201001T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/11
DESCRIPTION:Title: Chebyshev’s bias and sums of two squares\nby Lucile De
vin (University of Gothenburg) as part of ViBraNT (Virtual Brazilian Numbe
r Theory seminar)\n\n\nAbstract\nStudying the secondary terms of the Prime
Number Theorem in Arithmetic Progressions\, Chebyshev claimed that there
are more prime numbers congruent to 3 modulo 4 than to 1 modulo 4. We will
explain and qualify this claim following the framework of Rubinstein and
Sarnak. Then we will see how this framework can be adapted to other questi
ons on the distribution of prime numbers. This will be illustrated by a ne
w Chebyshev-like claim : there are “more” prime numbers that can be w
ritten as a sum of two squares with the even square larger than the odd sq
uare than the other way around.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitris Koukoulopoulos (Université de Montréal)
DTSTART:20201015T170000Z
DTEND:20201015T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/12
DESCRIPTION:Title: How concentrated can the divisors of a typical integer be?\nby Dimitris Koukoulopoulos (Université de Montréal) as part of ViBra
NT (Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nThe Delta func
tion measures the concentration of the sequence of divisors of an integer.
Specifically\, given an integer $n$\, we write $\\Delta(n)$ for the maxim
um over $y$ of the number of divisors of $n$ lying in the dyadic interval
$[y\,2y]$. It was introduced by Hooley in 1979 because of its connections
to various problems in Diophantine equations and approximation. In 1981\,
Maier and Tenenbaum proved that $\\Delta(n)>1$ for almost all integers $n$
\, thus settling a 1948 conjecture due to Erdös. In subsequent work\, the
y proved that $(\\log\\log n)^{c+o(1)}\\le \\Delta(n)\\le (\\log\\log n)^{
\\log2+o(1)}$\, where $c=(\\log2)/\\log(\\frac{1-1/\\log 27}{1-\\log3})\\a
pprox 0.33827$ for almost all integers $n$. In addition\, they conjectured
that $\\Delta(n)=(\\log\\log n)^{c+o(1)}$ for almost all $n$. In this tal
k\, I will present joint work with Ben Green and Kevin Ford that disproves
the Maier-Tenenbaum conjecture by replacing the constant $c$ in the lower
bound by another constant $c'=0.35332277\\dots$ that we believe is optima
l. We also prove analogous results about permutations and polynomials over
finite fields by reducing all three cases to an archetypal probabilistic
model.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Granville (Universite de Montréal)
DTSTART:20200917T170000Z
DTEND:20200917T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/13
DESCRIPTION:Title: Heuristics and computations for primes in short intervals\;
and sieves and Siegel zeros\nby Andrew Granville (Universite de Montr
éal) as part of ViBraNT (Virtual Brazilian Number Theory seminar)\n\n\nAb
stract\nWe describe joint work with Allysa Lumley in which we try to get a
n idea of the range of values the number of primes can take in an interval
of length y near to x. Our understanding is limited by our limited under
standing of the sieve and\, if we have time\, we will explain how that und
erstanding cannot be improved without showing that there are no Siegel zer
os\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bloom (Cambridge)
DTSTART:20201022T170000Z
DTEND:20201022T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/14
DESCRIPTION:Title: Additive structure in dense sets of integers\nby Thomas
Bloom (Cambridge) as part of ViBraNT (Virtual Brazilian Number Theory semi
nar)\n\n\nAbstract\nHow much additive structure can we guarantee in sets o
f integers\, knowing only their density? The study of which density thresh
olds are sufficient to guarantee the existence of various kinds of additiv
e structures is an old and fascinating subject with connections to analyti
c number theory\, additive combinatorics\, and harmonic analysis.\n\nIn th
is talk we will discuss recent progress on perhaps the most well-known of
these thresholds: how large do we need a set of integers to be to guarante
e the existence of a three-term arithmetic progression? In recent joint wo
rk with Olof Sisask we broke through the logarithmic density barrier for t
his problem\, establishing in particular that if a set is dense enough suc
h that the sum of reciprocals diverges\, then it must contain a three-term
arithmetic progression\, establishing the first case of an infamous conje
cture of Erdos.\n\nWe will give an introduction to this problem and sketch
some of the recent ideas that have made this progress possible. We will a
lso discuss a recent application to the density threshold of a set contain
ing no square differences.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Oxford)
DTSTART:20201008T170000Z
DTEND:20201008T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/15
DESCRIPTION:Title: An asymptotic version of the prime power conjecture for perf
ect difference sets\nby Sarah Peluse (Oxford) as part of ViBraNT (Virt
ual Brazilian Number Theory seminar)\n\n\nAbstract\nA subset D of a finite
cyclic group Z/mZ is called a "perfect difference set" if every nonzero e
lement of Z/mZ can be written uniquely as the difference of two elements o
f D. If such a set exists\, then a simple counting argument shows that m=n
^2+n+1 for some nonnegative integer n. Singer constructed examples of perf
ect difference sets in Z/(n^2+n+1)Z whenever n is a prime power\, and it i
s an old conjecture that these are the only such n for which a perfect dif
ference set exists. In this talk\, I will discuss a proof of an asymptotic
version of this conjecture: the number of n less than N for which Z/(n^2+
n+1)Z contains a perfect difference set is ~N/log(N).\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Ford (University of Illinois at Urbana-Champaign)
DTSTART:20201203T170000Z
DTEND:20201203T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/16
DESCRIPTION:Title: Divisors of integers\, permutations and polynomials\nby
Kevin Ford (University of Illinois at Urbana-Champaign) as part of ViBraNT
(Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nWe describe a pr
obabilistic model that describes the statistical behavior of the divisors
of integers\, divisors of permutations and divisors of polynomials over a
finite field. We will discuss how this can be used to obtain new bounds o
n the concentration of divisors of integers\, improving a result of Maier
and Tenenbaum. This is joint work with Ben Green and Dimitris Koukoulopou
los.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Maynard (Oxford)
DTSTART:20201029T170000Z
DTEND:20201029T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/17
DESCRIPTION:Title: Primes in arithmetic progressions to large moduli\nby Ja
mes Maynard (Oxford) as part of ViBraNT (Virtual Brazilian Number Theory s
eminar)\n\n\nAbstract\nI'll talk about some recent work extending the Bomb
ieri-Vinogradov Theorem to moduli larger than x^{1/2} provided the moduli
have a conveniently sized divisor. In different formulations\, this allows
us to handle moduli as large as x^{3/5}\, or allows for complete uniformi
ty with respect to the residue class as in the original Bombieri-Vinogrado
v theorem.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaisa Matomäki (University of Turku)
DTSTART:20201119T170000Z
DTEND:20201119T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/18
DESCRIPTION:Title: Almost primes in almost all very short intervals\nby Kai
sa Matomäki (University of Turku) as part of ViBraNT (Virtual Brazilian N
umber Theory seminar)\n\n\nAbstract\nBy probabilistic models one expects t
hat\, as soon as $h \\to \\infty$ with $X \\to \\infty$\, short intervals
of the type $(x- h \\log X\, x]$ contain primes for almost all $x \\in (X/
2\, X]$. However\, this is far from being established. In the talk I discu
ss related questions and in particular describe how to prove the above cla
im when one is satisfied with finding $P_2$-numbers (numbers that have at
most two prime factors) instead of primes.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksym Radziwill (Caltech)
DTSTART:20201112T170000Z
DTEND:20201112T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/19
DESCRIPTION:Title: The Fyodorov-Hiary-Keating conjecture\nby Maksym Radziwi
ll (Caltech) as part of ViBraNT (Virtual Brazilian Number Theory seminar)\
n\n\nAbstract\nI will discuss recent progress on the Fyodorov-Hiary-Keatin
g conjecture\non the distribution of the local maximum of the Riemann zeta
-function. This is joint\nwork with Louis-Pierre Arguin and Paul Bourgade.
\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Εfthymios Sofos (University of Glasgow)
DTSTART:20201105T170000Z
DTEND:20201105T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/20
DESCRIPTION:Title: Schinzel Hypothesis with probability 1 and rational points\nby Εfthymios Sofos (University of Glasgow) as part of ViBraNT (Virtua
l Brazilian Number Theory seminar)\n\n\nAbstract\nJoint work with Alexei S
korobogatov\, preprint: https://arxiv.org/abs/2005.02998. Schinzel's Hypot
hesis states that every integer polynomial satisfying certain congruence c
onditions represents infinitely many primes. It is one of the main problem
s in analytic number theory but is completely open\, except for polynomial
s of degree 1. We describe our recent proof of the Hypothesis for 100% of
polynomials (ordered by size of coefficients). We use this to prove that\,
with positive probability\, Brauer--Manin controls the Hasse principle fo
r Châtelet surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandoel Vieira (IMPA)
DTSTART:20201126T170000Z
DTEND:20201126T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/21
DESCRIPTION:Title: M\\L is not closed\nby Sandoel Vieira (IMPA) as part of
ViBraNT (Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nIn this t
alk we will describe joint work with C. G. Moreira\, C. Matheus and D. Lim
a in which we proved that $M\\setminus L$ is not a closed subset of $\\mat
hbb{R}$. For that\, we show that $1+3/\\sqrt{2}$ is a point of the Lagrang
e spectrum $L$ which is accumulated by a sequence of elements of the compl
ement $M\\setminus L$ of the Lagrange spectrum in the Markov spectrum $M$.
\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Ramaré (Aix-Marseille)
DTSTART:20210114T170000Z
DTEND:20210114T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/22
DESCRIPTION:Title: An additive question in multiplicative number theory\nby
Olivier Ramaré (Aix-Marseille) as part of ViBraNT (Virtual Brazilian Num
ber Theory seminar)\n\n\nAbstract\nWhile studying the representation of a
congruence class or a ray-class by a product of three small primes\, we st
umbled on an auxiliary additive combinatorics question involving sum-free
sets in finite abelian groups that seems to be new. The aim of the talk is
to present this question.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cathy Swaenepoel (Paris Diderot)
DTSTART:20210121T170000Z
DTEND:20210121T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/23
DESCRIPTION:Title: Prime numbers with preassigned digits\nby Cathy Swaenepo
el (Paris Diderot) as part of ViBraNT (Virtual Brazilian Number Theory sem
inar)\n\n\nAbstract\nBourgain (2015) estimated the number of prime numbers
with a proportion c>0 of preassigned digits in base 2 (c is an absolute c
onstant not specified). We present a generalization of this result in any
base $g\\geq2$ and we provide explicit admissible values for the proportio
n c depending on g. Our proof\, which adapts\, develops and refines Bourga
in’s strategy\, is based on the circle method and combines techniques fr
om harmonic analysis together with results on zeros of Dirichlet L-functio
ns\, notably a very strong zero-free region due to Iwaniec.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyle Pratt (Oxford)
DTSTART:20210128T170000Z
DTEND:20210128T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/24
DESCRIPTION:Title: Landau-Siegel zeros and central values of L-functions\nb
y Kyle Pratt (Oxford) as part of ViBraNT (Virtual Brazilian Number Theory
seminar)\n\n\nAbstract\nResearchers have tried for many years to eliminate
the possibility of Landau-Siegel zeros---certain exceptional counterexamp
les to the Generalized Riemann Hypothesis. Often one thinks of these zeros
as being a severe nuisance\, but there are many situations in which their
existence allows one to prove spectacular\, though illusory\, results. I
will review some of this history and some of these results. In the latter
portion of the talk I will discuss recent work\, joint with H. M. Bui and
Alexandru Zaharescu\, in which we show that the existence of Landau-Siegel
zeros has implications for the behavior of $L$-functions at the central p
oint.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Munsch (Graz)
DTSTART:20210204T170000Z
DTEND:20210204T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/25
DESCRIPTION:Title: Pair correlation of sequences: metric results and a modified
additive energy\nby Marc Munsch (Graz) as part of ViBraNT (Virtual Br
azilian Number Theory seminar)\n\n\nAbstract\nThe uniform distribution of
a sequence $\\{x_n\\}_{n\\geq 1}$ measures the pseudo-random behavior at a
global scale. At a more localized\nscale\, we can study the pair correlat
ion for sequences in the unit interval. Pseudo-random behavior with respec
t to this statistic is called Poissonian behavior. The metric theory of pa
ir correlations of sequences of the form $(a_n\\alpha)_{n \\geq 1}$ has b
een pioneered by Rudnick\, Sarnak and Zaharescu. Recently\, a general fram
ework was developed which gives a criterion for Poissonian pair correlatio
n of such sequences for almost $\\alpha \\in (0\,1)$\, in terms of the add
itive energy of the integer sequence $\\{a_n\\}_{n \\geq 1}$. In the prese
nt talk we will discuss a similar framework in the more delicate case wher
e $\\{a_n\\}_{n \\geq 1}$ is a sequence of reals. We give a criterion invo
lving a modified version of the additive energy expressed via a diophantin
e inequality. We give several concrete applications of our method and pres
ent some open problems. This is joint work with Christoph Aistleitner and
Daniel EL-Baz.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joni Teräväinen (Oxford)
DTSTART:20210211T170000Z
DTEND:20210211T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/26
DESCRIPTION:Title: Higher order uniformity of the Möbius function\nby Joni
Teräväinen (Oxford) as part of ViBraNT (Virtual Brazilian Number Theory
seminar)\n\n\nAbstract\nI will discuss recent work where we prove that th
e Möbius function is orthogonal to a wide class of phase functions (inclu
ding all polynomial phases) on almost all very short intervals. I will als
o discuss applications to superpolynomial word complexity for the Liouvill
e sequence and to a new averaged version of Chowla's conjecture. This is j
oint work with Kaisa Matomäki\, Maksym Radziwiłł\,Terence Tao and Tamar
Ziegler.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Weingartner (South Utah university)
DTSTART:20210218T170000Z
DTEND:20210218T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/27
DESCRIPTION:Title: An extension of the Siegel-Walfisz theorem\nby Andreas W
eingartner (South Utah university) as part of ViBraNT (Virtual Brazilian N
umber Theory seminar)\n\n\nAbstract\nWe extend the Siegel-Walfisz theorem
to a family of integer\nsequences that are characterized by constraints on
the size of the\nprime factors. Besides prime powers\, this family includ
es smooth\nnumbers\, almost primes and practical numbers.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caroline Turnage-Butterbaugh (Carleton college)
DTSTART:20210225T170000Z
DTEND:20210225T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/28
DESCRIPTION:Title: Gaps between zeros of the Riemann zeta-function\nby Caro
line Turnage-Butterbaugh (Carleton college) as part of ViBraNT (Virtual Br
azilian Number Theory seminar)\n\n\nAbstract\nLet $0 < \\gamma_1 \\le \\ga
mma_2 \\le \\cdots $ denote the\nordinates of the complex zeros of the Rie
mann zeta-function function\nin the upper half-plane. The average distance
between $\\gamma_n$ and\n$\\gamma_{n+1)$ is $2\\pi / \\log \\gamma_n$ as
$n\\to \\infty$. An\nimportant goal is to prove unconditionally that these
distances\nbetween consecutive zeros can much\, much smaller than the ave
rage for\na positive proportion of zeros. We will discuss the motivation b
ehind\nthis endeavor\, progress made assuming the Riemann Hypothesis\, and
\nrecent work with A. Simonič and T. Trudgian to obtain an unconditional\
nresult.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brad Rodgers (Queen’s University)
DTSTART:20210415T170000Z
DTEND:20210415T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/29
DESCRIPTION:Title: The distribution of random polynomials with multiplicative c
oefficients\nby Brad Rodgers (Queen’s University) as part of ViBraNT
(Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nA classic paper
of Salem and Zygmund investigates the distribution of trigonometric polyno
mials whose coefficients are chosen randomly (say +1 or -1 with equal prob
ability) and independently. Salem and Zygmund characterized the typical di
stribution of such polynomials (gaussian) and the typical magnitude of the
ir sup-norms (a degree N polynomial typically has sup-norm of size $\\sqrt
{N \\log N}$ for large N). In this talk we will explore what happens when
a weak dependence is introduced between coefficients of the polynomials\;
namely we consider polynomials with coefficients given by random multiplic
ative functions. We consider analogues of Salem and Zygmund's results\, ex
ploring similarities and some differences.\n\nSpecial attention will be gi
ven to a beautiful point-counting argument introduced by Vaughan and Woole
y which ends up being useful.\n\nThis is joint work with Jacques Benatar a
nd Alon Nishry.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Bettin (University of Genova)
DTSTART:20210311T170000Z
DTEND:20210311T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/30
DESCRIPTION:Title: Modularity and distribution of quantum knots invariants\
nby Sandro Bettin (University of Genova) as part of ViBraNT (Virtual Brazi
lian Number Theory seminar)\n\n\nAbstract\nWe consider Zagier's modularity
conjecture for the colored Jones\npolynomials of hyperbolic knots. We pro
ve this conjecture in some\ncases and show that\, in the case of the 4_1 k
not\, one can also deduce\na law of large for the values of the colored Jo
nes polynomial at roots\nof unity. This is joint work with Sary Drappeau.\
n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Mastrostefano (Warwick)
DTSTART:20210318T170000Z
DTEND:20210318T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/31
DESCRIPTION:Title: The partial sum of a random multiplicative function on integ
ers with a large prime factor\nby Daniele Mastrostefano (Warwick) as p
art of ViBraNT (Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nLe
t $f(n)$ be a Rademacher random multiplicative function. We prove that\, f
or any $\\epsilon>0$ and as $x\\rightarrow +\\infty$\, we almost surely ha
ve\n\n$\\sum_{n\\leq x\,\\\; \\\\ P(n)>\\sqrt{x}} f(n)\\ll\\sqrt{x}(\\log\
\log x)^{1/4+\\epsilon}\,$\n\nwhere $P(n)$ stands for the largest prime fa
ctor of $n$. \nThis is close to be sharp and gives an indication of the si
ze of the largest fluctuations of the full partial sum.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Aymone (UFMG)
DTSTART:20210408T170000Z
DTEND:20210408T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/34
DESCRIPTION:Title: Some oscillation theorems in analytic and probabilistic Numb
er Theory\nby Marco Aymone (UFMG) as part of ViBraNT (Virtual Brazilia
n Number Theory seminar)\n\n\nAbstract\nThis talk will be divided into two
independent parts. In the first part of the talk I will discuss the prime
number race mod 4: Usually one assumes standards conjectures as GRH to de
duce some results that captures the intuition behind the Tchébyshev bias
-- I will do the other way around. In the second part of the talk I will d
iscuss a recent work with Winston Heap and Jing Zhao on sign changes of th
e partial sums of a random multiplicative function.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Hughes (University of York)
DTSTART:20210325T170000Z
DTEND:20210325T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/35
DESCRIPTION:Title: A Random Matrix Model for Gram's Law\nby Chris Hughes (U
niversity of York) as part of ViBraNT (Virtual Brazilian Number Theory sem
inar)\n\n\nAbstract\nIt is well known that the counting function for the R
iemann\nzeta zeros\, N(T)\, has a smooth main term and a much smaller\ndis
continuous correction term\, S(T). Gram's Law is the observation\nthat bet
ween consecutive points where the smooth part of the counting\nfunction is
an integer\, there typically is exactly one zeta zero. This\n"Law" doesn'
t hold all the time\, and we will use random matrix theory\nto model the p
roportion of time the law holds for. The flavour of\nrandom matrix theory
that normally models the Riemann zeros is the\nunitary group. However\, st
udying Gram's Law requires the special\nunitary group\, where many of the
useful techniques for random unitary\nmatrices fail to hold. Much of this
work was done jointly with my\nformer PhD student Catalin Hanga.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youness Lamzouri (Institut Elie Cartan de Lorraine)
DTSTART:20210506T170000Z
DTEND:20210506T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/36
DESCRIPTION:Title: Zeros of linear combinations of L-functions near the critica
l line\nby Youness Lamzouri (Institut Elie Cartan de Lorraine) as part
of ViBraNT (Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nIn th
is talk\, I will present a recent joint work with Yoonbok Lee\, where we i
nvestigate the number of zeros of linear combinations of $L$-functions in
the vicinity of the critical line. More precisely\, we let $L_1\, \\dots\,
L_J$ be distinct primitive $L$-functions belonging to a large class (whic
h conjecturally contains all $L$-functions arising from automorphic repres
entations on $\\text{GL}(n)$)\, and $b_1\, \\dots\, b_J$ be real numbers.
Our main result is an asymptotic formula for the number of zeros of $F(\\s
igma+it)=\\sum_{j\\leq J} b_j L_j(\\sigma+it)$ in the region $\\sigma\\geq
1/2+1/G(T)$ and $t\\in [T\, 2T]$\, uniformly in the range $\\log \\log T
\\leq G(T)\\leq (\\log T)^{\\nu}$\, where $\\nu\\asymp 1/J$. This establis
hes a general form of a conjecture of Hejhal in this range. The strategy o
f the proof relies on comparing the distribution of $F(\\sigma+it)$ to tha
t of an associated probabilistic random model.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chantal David (Concordia University)
DTSTART:20210422T170000Z
DTEND:20210422T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/37
DESCRIPTION:Title: One-Level density for cubic characters over the Eisenstein f
ield\nby Chantal David (Concordia University) as part of ViBraNT (Virt
ual Brazilian Number Theory seminar)\n\n\nAbstract\nWe show that the one-l
evel density for $L$-functions associated with the cubic residue symbols $
\\chi_n$\, with $n \\in \\mathbb{Z}[\\omega]$ square-free\, satisfies the
Katz-Sarnak conjecture for all test functions whose Fourier transforms are
supported in $(-13/11\, 13/11)$\, under GRH. This is the first result ext
ending the support outside the trivial range $(-1\, 1)$ for a family of cu
bic $L$-functions. This implies that a positive proportion of the $L$-func
tions associated with these characters do not vanish at the central point
$s = 1/2$. A key ingredient is a bound on an average of generalized cubic
Gauss sums at prime arguments\, whose proof is based on the work of Heath-
Brown and Patterson.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Chen (National University of Singapore)
DTSTART:20210527T170000Z
DTEND:20210527T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/39
DESCRIPTION:Title: A probabilistic approach to the Erdös-Kac theorem for addit
ive functions\nby Louis Chen (National University of Singapore) as par
t of ViBraNT (Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nWe p
resent a new approach to assessing the rates of convergence to the Gaussia
n and Poisson distributions in the Erdös-Kac theorem for additive arithme
tic functions of a random integer. Our approach is probabilistic\, working
directly on spaces of random variables without any use of Fourier analyti
c methods. Of the methods we used is Stein’s method. Our results general
ize the existing ones in the literature. This talk is based on joint work
with Arturo Jaramillo and Xiaochuan Yang.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anders Södergren (Chalmers)
DTSTART:20210610T170000Z
DTEND:20210610T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/40
DESCRIPTION:Title: Can a random lattice and its dual be independent?\nby An
ders Södergren (Chalmers) as part of ViBraNT (Virtual Brazilian Number Th
eory seminar)\n\n\nAbstract\nIn this talk I will discuss Rogers' mean valu
e formula in the space of unimodular lattices as well as a recent generali
zation of Rogers' formula. In particular\, I will describe a formula for m
ean values of products of Siegel transforms with arguments taken from both
a lattice and its dual lattice. The main application is a result on the j
oint distribution of the vector lengths in a random lattice and its dual l
attice in the limit as the dimension of the lattices tends to infinity\, a
nd provides a partial affirmative answer to the question in the title. Thi
s is joint work with Andreas Strömbergsson.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fiorilli (CNRS)
DTSTART:20210513T170000Z
DTEND:20210513T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/41
DESCRIPTION:Title: Higher moments of primes in intervals and in arithmetic prog
ressions\nby Daniel Fiorilli (CNRS) as part of ViBraNT (Virtual Brazil
ian Number Theory seminar)\n\n\nAbstract\nSince the work of Selberg and of
Barban\, Davenport and\nHalberstam\, the variances of primes in intervals
and in arithmetic\nprogressions has been widely studied and continue to b
e an active topic\nof research. However\, much less is known about higher
moments. Hooley\nestablished a bound on the third moment in progressions\
, which was\nlater sharpened by Vaughan for a variant involving a major ar
cs\napproximation. Little is known for moments of order four or higher\,\n
other than the conjecture of Hooley and the conditional result of\nMontgom
ery-Soundararajan. In this talk I will discuss recent joint work\nwith Ré
gis de la Bretèche on weighted moments in short intervals and on\nweighte
d moments of moments in progressions. In particular we will show\nhow to d
educe sharp unconditional omega results on all weighted even\nmoments in c
ertain ranges.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vorrapan Chandee (KSU)
DTSTART:20210603T170000Z
DTEND:20210603T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/42
DESCRIPTION:Title: The sixth moment of Dirichlet L-functions without average in
the t-aspect\nby Vorrapan Chandee (KSU) as part of ViBraNT (Virtual B
razilian Number Theory seminar)\n\n\nAbstract\nWe prove an asymptotic for
the sixth moment of Dirichlet L-functions averaged over primitive characte
rs modulo q\, over all moduli q <= Q. Unlike the previous work of Conrey\,
Iwaniec\, and Soundararajan\, we do not need to include an average on the
critical line\, thus requiring treatment of the "unbalanced" sums. This i
s a joint work with Xiannan Li\, Kaisa Matomaki\, and Maksym Radziwill.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sávio Ribas (UFOP)
DTSTART:20210520T170000Z
DTEND:20210520T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/44
DESCRIPTION:Title: Some direct and inverse zero-sum problems\nby Sávio Rib
as (UFOP) as part of ViBraNT (Virtual Brazilian Number Theory seminar)\n\n
\nAbstract\nIn this talk\, we will introduce the main zero-sum problems in
additive combinatorics. In particular\, we will define the Davenport and
the Erdös-Ginzburg-Ziv constants\, among other similar constants for fini
te groups. We will also present their main results so far and Gao's conjec
ture that connects some of these constants (which has already been proven
for abelian groups). In addition\, we will present the similar weighted pr
oblems and the inverse problems. This is a joint work with D.V. Avelar\, F
.E. Brochero Martínez\, A. Lemos and B.K. Moryia.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Misturini (UFRGS)
DTSTART:20210617T170000Z
DTEND:20210617T180000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/45
DESCRIPTION:Title: Law of the Iterated Logarithm for a Random Dirichlet Series<
/a>\nby Ricardo Misturini (UFRGS) as part of ViBraNT (Virtual Brazilian Nu
mber Theory seminar)\n\n\nAbstract\nWe consider the random Dirichlet serie
s F(σ) obtained when\, in each term of the sum that defines the Riemann Z
eta function ζ(σ)\, we put + or - signs chosen independently and uniform
ly at random. This series converges when σ > 1/2. We study the behavior o
f F(σ) when σ goes to 1/2\, providing a Law of the Iterated Logarithm\,
which describes the magnitude of the fluctuations of F(σ). This is a join
t work with Marco Aymone and Susana Frómeta.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Shparlinski (UNSW)
DTSTART:20221004T160000Z
DTEND:20221004T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/46
DESCRIPTION:Title: Maximal Operators and Restriction Bounds for Weyl Sums\n
by Igor Shparlinski (UNSW) as part of ViBraNT (Virtual Brazilian Number Th
eory seminar)\n\n\nAbstract\nhttps://w3.impa.br/~goncalves/assets/files/Sh
parlinskiAbstract.pdf\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Ramaré (Marseillle)
DTSTART:20221011T160000Z
DTEND:20221011T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/47
DESCRIPTION:Title: The Levin-Fainleib pathway\, around and further\nby Oliv
ier Ramaré (Marseillle) as part of ViBraNT (Virtual Brazilian Number Theo
ry seminar)\n\n\nAbstract\nWe shall describe three occurrences of a device
introduced by Levin and Fainleib in 1967 and go on to present a recent ex
tension of one of these\, which results from a collaboration with Alisa Se
dunova and Ritika Sharma.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Winston Heap
DTSTART:20221018T160000Z
DTEND:20221018T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/48
DESCRIPTION:Title: Mean values of long Dirichlet polynomials\nby Winston He
ap as part of ViBraNT (Virtual Brazilian Number Theory seminar)\n\n\nAbstr
act\nWe first survey some applications of mean value results for Dirichlet
polynomials over primes in the theory of the Riemann zeta function. This
includes Selberg's central limit theorem/value distribution and the pair
correlation of zeros. We highlight a common obstacle in these areas which
is that of longer sums and how they usually require the assumption of the
twin-prime conjectures when computing their mean values. We then give some
examples showing how\, on the assumption of the Riemann hypothesis\, one
can compute asymptotics for moments of long sums without such conjectures
.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Mangerel (Durham)
DTSTART:20221025T160000Z
DTEND:20221025T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/49
DESCRIPTION:Title: Large order Dirichlet characters and an analogue of a conjec
ture of Vinogradov\nby Alexander Mangerel (Durham) as part of ViBraNT
(Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nLet $q$ be a larg
e prime. It is an old and classical problem to understand\nthe distributio
n of quadratic residues and non-residues modulo $q$. According\nto an old
and famous conjecture of I.M. Vinogradov\, the least quadratic\nnon-residu
e n modulo q should satisfy $n \\leq q^c$ for any positive $c > $0\, when\
n$q$ is large enough. This statement would be implied by non-trivial upper
\nbounds for averages of the Legendre symbol $\\left( \\frac{n}{q}\\right)
$ with $n \\leq q^c.$ Currently\nthe best such results\, due essentially t
o Burgess\, are satisfactory only\nwhen $c > 1/4$\, due to the potential o
bstruction\, difficult to rule out\, that\n$\\left( \\frac{n}{q}\\right) =
+1$ for many initial integers n.\n\nIn this talk I will discuss a general
isation of Vinogradov's conjecture to\nother primitive Dirichlet character
s \\chi modulo q\, seeking the least n for\nwhich $\\chi(n)$ is not $1$. I
will explain some recent work of mine that shows\,\nusing techniques from
additive combinatorics\, that when the order d of $\\chi$\ngrows with q t
he aforementioned obstruction does not occur\, that the\nanalogue of Vinog
radov's conjecture for $\\chi$ does hold\, and that moreover\n$\\chi(n) =
1$ with $n \\leq q^c$ is in fact a rare event for all $c > 0$. I will\nals
o discuss some results related to showing cancellation in short sums of\n$
\\chi(n)$ with $n \\leq q^c$ for $c > 0$ arbitrarily small\, going beyond
Burgess'\nestimate.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Xu (Stanford)
DTSTART:20221101T160000Z
DTEND:20221101T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/50
DESCRIPTION:Title: Central limit theorems for random multiplicative functions\nby Max Xu (Stanford) as part of ViBraNT (Virtual Brazilian Number Theo
ry seminar)\n\n\nAbstract\nIn joint work with Kannan Soundararajan\, we co
nsider the behavior of random multiplicative functions when summed over su
bsets of the integers in [1\, N]\, and give several examples of sets where
such sums satisfy a central limit theorem. In contrast\, as we know from
the work of Harper\, the partial sums over all integers in [1\, N] do not
satisfy a central limit theorem.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cynthia Bortolotto (Zurich)
DTSTART:20221115T160000Z
DTEND:20221115T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/51
DESCRIPTION:Title: Weyl sums with Multiplicative Coefficients and Joint Equidis
tribution\nby Cynthia Bortolotto (Zurich) as part of ViBraNT (Virtual
Brazilian Number Theory seminar)\n\n\nAbstract\nIn 1964\, Hooley proved th
at for an irreducible polynomial p in Z[x]\, the ratios v/n for v roots of
the polynomial p modulo n\, are equidistributed modulo 1. We prove joint
equidistribution of these roots of polynomial congruences and polynomial v
alues. As part of the proof\, we generalize a result of Montgomery and Vau
ghan regarding exponential sums with multiplicative coefficients to the se
tting of Weyl sums.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Pagano (Concordia)
DTSTART:20221129T160000Z
DTEND:20221129T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/52
DESCRIPTION:Title: The negative Pell equation\nby Carlo Pagano (Concordia)
as part of ViBraNT (Virtual Brazilian Number Theory seminar)\n\n\nAbstract
\nIn 1995\, Peter Stevenhagen made a conjecture about the number of square
-free positive integers d up to X such that the negative Pell equation att
ached to d admits a solution in the integers. I will present a joint work
with Peter Koymans resolving this conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Aisleitner (TU Graz)
DTSTART:20221108T160000Z
DTEND:20221108T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/53
DESCRIPTION:Title: A first guide to uniform distribution mod 1 and discrepancy<
/a>\nby Christoph Aisleitner (TU Graz) as part of ViBraNT (Virtual Brazili
an Number Theory seminar)\n\n\nAbstract\nThe foundations for the theory of
uniform distribution modulo 1 were laid in Hermann Weyl's seminal paper o
f 1916. Originally motivated by questions from Diophantine approximation\,
it turned out that the concept of uniform distribution is connected with
many other mathematical areas\, including exponential sums\, ergodic theor
y\, and numerical analysis. This is a survey talk\, where we will sketch s
ome of the basic concepts and results of the theory. Keywords are: Kroneck
er sequences\, pseudorandomness\, Erdös-Turan inequality\, Koksma inequal
ity\, and Roth's theorem. In the end we give a brief exposition on how thi
s machinery was applied in very recent work of the author (jointly with Be
nce Borda and Manuel Hauke\, arXiv:2210.14095) on the distribution of part
ial quotients of reduced fractions with fixed denominator.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Klurman (Bristol)
DTSTART:20221122T160000Z
DTEND:20221122T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/54
DESCRIPTION:Title: Automatic semigroups\nby Oleksiy Klurman (Bristol) as pa
rt of ViBraNT (Virtual Brazilian Number Theory seminar)\n\n\nAbstract\nThe
main goal of the talk is to discuss recent progress in our understanding
of the following general phenomena: how does multiplicative structure corr
elate with "automaticity"? No preliminary background is required. This is
based on a joint work with J. Konieczny.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Destagnol (Paris-Saclay)
DTSTART:20221206T160000Z
DTEND:20221206T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/55
DESCRIPTION:Title: The Loughran--Smeets conjecture for some Châtelet type vari
eties\nby Kevin Destagnol (Paris-Saclay) as part of ViBraNT (Virtual B
razilian Number Theory seminar)\n\n\nAbstract\nSerre in 1990 started a res
earch program aiming to understand the probability that a randomly chosen
diophantine equation has a solution over Q. Most cases of the problem are
still open today\, even when the equations satisfy the Hasse principle but
the Loughran--Smeets conjectures give predictions for that probability in
certain cases.\nI will report on joint work with Efthymios Sofos regardin
g this problem for x^2-Dy^2=P_1(t)...P_R(t)z^2 where D is a square-free in
teger and P_i are fixed integer polynomials of any degree in n variables\,
with n relatively large compared to the degrees of the P_i.\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayla Gafni (Mississipi)
DTSTART:20221213T160000Z
DTEND:20221213T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/56
DESCRIPTION:by Ayla Gafni (Mississipi) as part of ViBraNT (Virtual Brazili
an Number Theory seminar)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Greenfeld (Princeton)
DTSTART:20230110T160000Z
DTEND:20230110T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/57
DESCRIPTION:by Rachel Greenfeld (Princeton) as part of ViBraNT (Virtual Br
azilian Number Theory seminar)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Vaaler (Austin)
DTSTART:20230124T160000Z
DTEND:20230124T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/58
DESCRIPTION:by Jeffrey Vaaler (Austin) as part of ViBraNT (Virtual Brazili
an Number Theory seminar)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stevan Gajovic (Max Planck)
DTSTART:20230131T160000Z
DTEND:20230131T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/59
DESCRIPTION:by Stevan Gajovic (Max Planck) as part of ViBraNT (Virtual Bra
zilian Number Theory seminar)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaisa Matomäki (Turku)
DTSTART:20230207T160000Z
DTEND:20230207T170000Z
DTSTAMP:20260404T110830Z
UID:NumberTheory2/60
DESCRIPTION:by Kaisa Matomäki (Turku) as part of ViBraNT (Virtual Brazili
an Number Theory seminar)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NumberTheory2/60/
END:VEVENT
END:VCALENDAR