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BEGIN:VEVENT
SUMMARY:Chandrashekhar Khare
DTSTART:20200608T160000Z
DTEND:20200608T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/1
DESCRIPTION:Title: Serre-type conjectures for projective representations\nby Chand
rashekhar Khare as part of Upstate New York Online Number Theory Colloquiu
m\n\n\nAbstract\nWe consider automorphy of many representations of the fo
rm $\\bar \\rho:G_K \\rightarrow PGL_2(k)$ with $K$ a CM field and $k=F_3\
,F_5$. In particular we prove (under some mild conditions) that for $F$ t
otally real\, a surjective representation $\\bar \\rho:G_F \\rightarrow P
GL_2(F_5)$ with totally odd sign character arises from a Hilbert modular
form of weight $(2\,\\ldots\, 2)$. This is joint work with Patrick Allen a
nd Jack Thorne.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Mornev
DTSTART:20200622T160000Z
DTEND:20200622T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/2
DESCRIPTION:Title: Tate conjectures in function field arithmetic\nby Maxim Mornev
as part of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\
nMany versions of Tate conjectures were proved for Drinfeld modules and\nf
or their higher-dimensional generalizations\, the t-modules of Anderson.\n
The underpinning of this success is a technically simple but powerful\nthe
ory of t-motives pioneered by Anderson. In this talk I shall describe\nan
approach to Tate conjectures for t-modules which implies all the\nknown ve
rsions and explains why some variants of the conjectures fail.\nThe approa
ch combines the theory of t-motives with the t-adic\ncounterpart of the th
eory of overconvergent F-isocrystals.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Sprung
DTSTART:20200706T180000Z
DTEND:20200706T190000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/3
DESCRIPTION:Title: Subleading terms of L-functions of elliptic curves\nby Florian
Sprung as part of Upstate New York Online Number Theory Colloquium\n\n\nAb
stract\nThe leading term of the L-function of an elliptic curve encodes\ns
ome of its arithmetic via BSD. What about the subleading term? Wuthrich\np
roved that this subleading term is related to the leading one as a\nconseq
uence of the functional equation. Bianchi gave a p-adic analogue of\nthis
result\, and also found another consequence of the functional equation\nco
ncerning Iwasawa's mu-invariant\, assuming p is ordinary. This talk\nprese
nts joint work with C. Dion\, in which we extend the results of\nBianchi/W
uthrich in various directions: First\, we discuss what happens in\nthe sup
ersingular (not ordinary) case. In this case\, there is a pair of\namenabl
e functions\, for which we prove Bianchi's/Wuthrich's ideas can be\napplie
d. Since we now have a pair of functions\, we can do something new: We\nca
n relate their orders of vanishing to each other. If there is time\, we\na
lso hope to discuss a result concerning lambda-invariants (for which p can
\nbe ordinary or supersingular).\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Filaseta
DTSTART:20200720T160000Z
DTEND:20200720T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/4
DESCRIPTION:Title: On a dense universal Hilbert set\nby Michael Filaseta as part o
f Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nA $unive
rsal\\ Hilbert\\ set$\nis an infinite set $\\mathcal S \\subseteq \\math
bb Z$\nhaving the property that for every $F(x\,y) \\in \\mathbb Z[x\,y]$\
nwhich is irreducible in $\\mathbb Q[x\,y]$ and satisfies $\\deg_{x} (F) \
\ge 1$\, \nwe have that for all but finitely many $y_{0} \\in \\mathcal
S$\, the polynomial \n$F(x\,y_{0})$ is irreducible in $\\mathbb Q[x]$. \n
The existence of universal Hilbert sets is due to P.C. Gilmore and A. Robi
nson in 1955\,\nand since then a number of explicit examples have been giv
en. \nUniversal Hilbert sets of density $1$ in the integers have been sho
wn to exist \nby Y. Bilu in 1996 and P. D\\`ebes and U. Zannier in 1998.\n
In this talk\, we discuss a connection between universal Hilbert sets and
\nSiegel's Lemma on the finiteness of integral points on a curve\nof genus
$\\ge 1$\, and explain how a result of K.Ford (2008) implies\nthe existen
ce of a universal Hilbert set $\\mathcal S$ satisfying\n\\[\n|\\{ m \\in \
\mathbb Z: m \\not\\in \\mathcal S\, |m| \\le X \\}| \\ll \\dfrac{X}{(\\lo
g X)^{\\delta}}\,\n\\]\nwhere $\\delta = 1 - (1+\\log\\log 2)/(\\log 2) =
0.086071\\ldots$. This is joint work with Robert Wilcox.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daqing Wan
DTSTART:20200803T160000Z
DTEND:20200803T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/5
DESCRIPTION:Title: Slopes in Z_p-towers of curves\nby Daqing Wan as part of Upstat
e New York Online Number Theory Colloquium\n\n\nAbstract\nThis is an expos
itory lecture. We shall review basic questions\, results and ideas on slop
es for zeta functions of curves over finite fields of characteristic p. Th
e emphasis will be on the slope variation when the curve varies in a $Z_p$
-tower.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Granville
DTSTART:20200817T160000Z
DTEND:20200817T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/6
DESCRIPTION:Title: Understanding the distribution of primes in (very) short intervals<
/a>\nby Andrew Granville as part of Upstate New York Online Number Theory
Colloquium\n\n\nAbstract\nIn joint work with Alyssa Lumley we explore the
maximum number\nof primes in short intervals\, both from a heuristic and a
computational\npoint-of-view. This leads naturally to questions in sieve
theory and\nprobability theory which we will also explore.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Clausen
DTSTART:20200831T160000Z
DTEND:20200831T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/7
DESCRIPTION:Title: On the quadratic reciprocity law\nby Dustin Clausen as part of
Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nI'll descr
ibe a rather idiosyncratic proof of the quadratic reciprocity\nlaw. This
talk can also be seen as a small introduction to algebraic K-theory and\nt
he use of homotopy theory in arithmetic.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hé\;lè\;ne Esnault
DTSTART:20200928T160000Z
DTEND:20200928T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/8
DESCRIPTION:Title: Bounding ramification with covers and curves\nby Hé\;l&eg
rave\;ne Esnault as part of Upstate New York Online Number Theory Colloqui
um\n\n\nAbstract\nIn positive characteristic\, there is no curve with the
property that its fundamental\ngroup covers the one of a given variety $X$
(Lefschetz property). Deligne asked\nwhether over an algebraically closed
field there is such a curve which preserves the\nmonodromy groups of ${\
\bar \\mathbb{Q}}_\\ell$ local systems in bounded rank and\nramification o
n $X$. We can not prove this in general\, instead we give weaker\nstateme
nts which enable one to tamify local systems. \n\nJoint work with Vasudeva
n Srinivas.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wadim Zudilin
DTSTART:20200914T160000Z
DTEND:20200914T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/9
DESCRIPTION:Title: Creative microscoping\nby Wadim Zudilin as part of Upstate New
York Online Number Theory Colloquium\n\n\nAbstract\nLet $A_k=2^{-6k}{\\bin
om{2k}k}^3$ for $k=0\,1\,\\dots$\,.\nThough traditional techniques of esta
blishing the hypergeometric evaluation\n\n$\\sum \\limits_{k=0}^\\infty(-1
)^k(4k+1)A_k =\\frac2\\pi$\n\nand (super)congruences\n\n$\\sum \\limits_{k
=0}^{p-1}(-1)^k(4k+1)A_k \\equiv p(-1)^{(p-1)/2}\\pmod{p^3} \\quad\\text{f
or\nprimes}\\\; p>2$\n\nshare certain similarities\, they do not display i
ntrinsic reasons for the two to be\nrelated.\nIn my talk I will outline ba
sic ingredients of a method developed in joint works\nwith Victor Guo\, wh
ich does the missing part\, also for many other instances of such\narithme
tic duality.\nThe main idea is constructing suitable $q$-deformations of t
he infinite sum (and\nmany such sums are already recorded in the $q$-liter
ature)\,\nand then look at the asymptotics of that at roots of unity.\nInt
erestingly enough\, the $q$-deformations may offer more.\nFor example\, th
e $q$-deformation of the above infinite sum also implies\n$$\n\\sum_{k=0}^
\\infty A_k\n=\\frac{\\Gamma(1/4)^4}{4\\pi^3}\n=\\frac{8L(f\,1)}{\\pi}\n\\
quad\\text{and}\\quad\n\\sum_{k=0}^{p-1}A_k\\equiv a(p)\\pmod{p^2}\n$$\n(i
n fact\, the latter congruences in their stronger modulo $p^3$ form proven
by Long\nand Ramakrishna)\,\nwhere $a(p)$ is the $p$-th Fourier coefficie
nt of (the weight 3 modular form)\n$f=q\\prod_{m=1}^\\infty(1-q^{4m})^6$.\
n\n($NB:$ The variable $q$ in the last definition is related to the modula
r\nparameter $\\tau$ through $q=e^{2\\pi i\\tau}$ and has nothing to do wi
th the $q$ in\nthe $q$-deformation.)\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel Waldschmidt
DTSTART:20201012T160000Z
DTEND:20201012T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/10
DESCRIPTION:Title: Some variants of Seshadri's constant\nby Michel Waldschmidt as
part of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nS
eshadri's constant is related to a conjecture due to Nagata. Another conje
cture\,\nalso due to Nagata and solved by Bombieri in 1970\, is related wi
th algebraic values\nof meromorphic functions. The main argument of Bombie
ri's proof leads to a Schwarz\nLemma in several variables\, the proof of w
hich gives rise to another invariant\nassociated with symbolic powers of t
he ideal of functions vanishing on a finite set\nof points. This invariant
is an asymptotic measure of the least degree of a\npolynomial in several
variables with given order of vanishing on a finite set of\npoints. Recent
works on the resurgence of ideals of points and the containment\nproblem
compare powers and symbolic powers of ideals.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chantal David
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/11
DESCRIPTION:Title: Moments and non-vanishing of cubic Dirichlet L-functions at s=1/2<
/a>\nby Chantal David as part of Upstate New York Online Number Theory Col
loquium\n\n\nAbstract\nA famous conjecture of Chowla predicts that $L(\\fr
ac{1}{2}\,\\chi)\\neq 0$ for all Dirichlet L-functions\nattached to primi
tive characters $\\chi$. It was conjectured first in the case where $\\chi
$ is a quadratic\ncharacter\, which is the most studied case. For quadrati
c Dirichlet L-functions\, Soundararajan\nproved that at least 87.5% of the
quadratic Dirichlet L-functions do not vanish at $s=\\frac{1}{2}.$\n\nUnd
er GRH\, there are slightly stronger results by Ozlek and Snyder.\nWe pres
ent in this talk the first result showing a positive proportion of cubic D
irichlet\nL-functions non-vanishing at s = 1/2 for the non-Kummer case ove
r function fields. This\ncan be achieved by using the recent breakthrough
work on sharp upper bounds for moments\nof Soundararajan\, Harper and Lest
er-Radziwill. Our results would transfer over number\nfields (but we would
need to assume GRH in this case).\nThe talk will be accessible to a gener
al audience of number theorists and graduate students\nin number theory.\n
\nJoint work with A. Florea and M. Lalin.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Buium
DTSTART:20201123T170000Z
DTEND:20201123T180000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/12
DESCRIPTION:Title: Solutions to arithmetic differential equations in the p-adic compl
ex field\nby Alexandru Buium as part of Upstate New York Online Number
Theory Colloquium\n\n\nAbstract\nArithmetic differential equations are an
alogues of differential equations\nin which derivatives of functions are r
eplaced by Fermat quotients of numbers.\nIn its original form this theory
would only allow the consideration of solutions to\nsuch equations in unr
amified extensions of the p-adic integers. Recently\, L.Miller\nand the au
thor showed that the `main examples' of arithmetic differential equations\
nin the theory possess a remarkable differential overconvergence property.
This\nallows the consideration (and study) of their solutions in the ring
of integers of\nthe p-adic complex field.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Baker
DTSTART:20201207T170000Z
DTEND:20201207T180000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/13
DESCRIPTION:Title: The Algebra of Forgetfulness\nby Matt Baker as part of Upstate
New York Online Number Theory Colloquium\n\n\nAbstract\nThere are a sever
al theorems in algebra where one purposely forgets\ncertain information ab
out the coefficients of a polynomial and then sees whether\ncertain proper
ties of the roots can still be determined. A prototypical example is\nDesc
artes’ Rule of Signs\, where we forget everything about a polynomial P e
xcept for\nthe signs of its coefficients and then ask for information abou
t the signs of the\nreal roots of P. I will explain a novel algebraic fram
ework for systematically\nunderstanding results of this type. As time perm
its\, I will discuss connections to\nmatroid theory\, including the algebr
aic foundations underlying the construction of a\n"moduli space of matroid
s". This is joint work with Oliver Lorscheid.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Larsen
DTSTART:20210222T170000Z
DTEND:20210222T180000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/14
DESCRIPTION:Title: Elliptic curves over fields with finitely generated Galois groups<
/a>\nby Michael Larsen as part of Upstate New York Online Number Theory Co
lloquium\n\n\nAbstract\nLet K be a field in characteristic 0 with $Gal (\\
bar{K}/K)$\nfinitely generated. What can be said about the group of ration
al points\nof an elliptic curve E over K? I will discuss various approache
s to this\nproblem\, via algebraic geometry\, algebraic combinatorics\, an
d analytic\nnumber theory.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerard van der Geer
DTSTART:20210308T170000Z
DTEND:20210308T180000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/15
DESCRIPTION:Title: Modular forms and invariant theory\nby Gerard van der Geer as
part of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nSi
egel and Teichmueller modular forms of genus g are generalizations\nof the
usual elliptic modular forms\, the case g=1\, but live on the\nmoduli spa
ces of abelian varieties and curves of genus g. These forms\, \nare just a
s intriguing\, but more difficult to construct.\nWe intend to show how one
can use invariant theory to describe in \nprinciple all such modular form
s for genus 2 and 3 explicitly.\nThis is joint work with Fabien Clery and
Carel Faber.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Harbater
DTSTART:20210322T160000Z
DTEND:20210322T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/16
DESCRIPTION:Title: Local-global principles over semi-global fields\nby David Harb
ater as part of Upstate New York Online Number Theory Colloquium\n\n\nAbst
ract\nLocal-global principles have classically been studied in the \nconte
xt of global fields\; i.e.\, number fields or function fields of \ncurves
over finite fields. In recent years\, they have also been studied \nover
what have come to be known as semi-global fields\, a class that \nincludes
function fields of p-adic curves. Classical results such as the \nHasse-M
inkowski theorem have been carried over to this context\, though \nwith ve
ry different proofs. The talk will present results in this \ndirection\, i
ncluding ongoing work of the speaker with J-L. \nColliot-Thélène\, J. Ha
rtmann\, D. Krashen\, R. Parimala\, and V. Suresh.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Pop
DTSTART:20210405T160000Z
DTEND:20210405T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/17
DESCRIPTION:Title: Towards minimalistic forms of the Neukirch and Uchida Theorem\
nby Florian Pop as part of Upstate New York Online Number Theory Colloquiu
m\n\n\nAbstract\nRecall that the famous Neukirch and Uchida Theorem (and i
ts variants) show that the isomorphism type of global fields is functorial
ly encoded in their absolute and/or solvable Galois theory. Inspired by th
e very recent work of Saidi-Tamagawa on the topic\, and work by Harry Smit
related to the subject\, I will present some work in progress on quite "m
inimalistic" forms of the Neukirch and Uchida Theorem and its generalizati
ons. This work in progress is collaboration with Adam Topaz.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Tschinkel
DTSTART:20210419T160000Z
DTEND:20210419T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/18
DESCRIPTION:Title: Equivariant birational types\nby Yuri Tschinkel as part of Ups
tate New York Online Number Theory Colloquium\n\n\nAbstract\nI will discus
s new results and constructions in equivariant birational geometry.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minhyong Kim
DTSTART:20210503T160000Z
DTEND:20210503T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/19
DESCRIPTION:Title: Recent Progress on Diophantine Equations in Two Variables\nby
Minhyong Kim as part of Upstate New York Online Number Theory Colloquium\n
\n\nAbstract\nThe study of rational or integral solutions to polynomial eq
uations $f(x_1\, x_2\,..\, x_n)=0$ is among the oldest subjects in mathema
tics. After a brief description of its modern history\, we will review a f
ew of the breakthroughs of the last few decades and some recent geometric
approaches to describing sets of solutions when the number of variables is
2.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Bell
DTSTART:20210517T160000Z
DTEND:20210517T170000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/20
DESCRIPTION:Title: Transcendental dynamical degrees of birational maps\nby Jason
Bell as part of Upstate New York Online Number Theory Colloquium\n\n\nAbst
ract\nThe degree of a dominant rational map $f:\\mathbb{P}^n\\to \\mathbb{
P}^n$ is\nthe common degree of its homogeneous components. By considering
iterates of $f$\,\none can form a sequence ${\\rm deg}(f^n)$\, which is s
ubmultiplicative and hence has\nthe property that there is some $\\lambda\
\ge 1$ such that $({\\rm deg}(f^n))^{1/n}\\to\n\\lambda$. The quantity $\
\lambda$ is called the first dynamical degree of $f$. \nWe’ll give an ov
erview of the significance of the dynamical degree in complex\ndynamics an
d describe recent examples in which this dynamical degree is provably\ntra
nscendental. This is joint work with Jeffrey Diller\, Mattias Jonsson\, a
nd Holly\nKrieger.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dino Lorenzini
DTSTART:20211108T183000Z
DTEND:20211108T193000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/21
DESCRIPTION:Title: Torsion and Tamagawa numbers\nby Dino Lorenzini as part of Ups
tate New York Online Number Theory Colloquium\n\n\nAbstract\nAssociated wi
th an abelian variety $A/K$ over a number field $K$ is a finite\nset of in
tegers greater than $1$ called the local Tamagawa numbers of $A/K$. Assumi
ng\nthat the abelian variety $A/K$ has a $K$-rational torsion point of pri
me order $N$\, we can\nask whether it is possible for none of the local Ta
magawa numbers to be divisible by\n$N$. The ratio $\\textrm{(product of th
e Tamagawa numbers)}/ |\\textrm{Torsion in }E(K) |$ appears in the\nconjec
tural leading term of the L-function of $A$ in the Birch and Swinnerton-Dy
er\nconjecture\, and we are thus interested in understanding whether there
are often\ncancellation in this ratio.\n\nWe will present some finiteness
results on this question in the case of elliptic\ncurves. More precisely\
, let $d > 0$ be an integer\, and assume that there exist\ninfinitely many
fields $K/\\mathbb{Q}$ of degree $d$ with an elliptic curve $E/K$ having
a $K$-rational\npoint of order $N$. We will show that for certain such pai
rs $(d\,N)$\, there are only\nfinitely many fields $K/\\mathbb{Q}$ of degr
ee $d$ such that there exists an elliptic curve $E/K$\nhaving a $K$-ration
al point of order $N$ and none of the local Tamagawa numbers are\ndivisibl
e by $N$. The lists of known exceptions are surprisingly small when $d$ is
at\nmost $7$.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Winnie Li
DTSTART:20211011T173000Z
DTEND:20211011T183000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/22
DESCRIPTION:Title: Pair arithmetical equivalence for quadratic fields\nby Winnie
Li as part of Upstate New York Online Number Theory Colloquium\n\n\nAbstra
ct\nGiven two nonisomorphic number fields K and M\, and two finite \norder
Hecke characters $\\chi$ of K and $\\eta$ of M respectively\, we say \nth
at the pairs $(\\chi\, K)$ and $(\\eta\, M)$ are arithmetically equivalent
\nif the associated L-functions coincide: $L(s\, \\chi\, K) = L(s\, \\eta
\, M)$. \nWhen the characters are trivial\, this reduces to the question o
f fields \nwith the same Dedekind zeta function\, investigated by Gassmann
in 1926\, \nwho found such fields of degree 180\, and by Perlis in 1977 a
nd others\, \nwho showed that there are no arithmetically equivalent field
s of degree \nless than 7.\n\nIn this talk we discuss arithmetically equiv
alent pairs where the fields \nare quadratic. They give rise to dihedral a
utomorphic forms induced from \ncharacters of different quadratic fields.
We characterize when a given \npair is arithmetically equivalent to anothe
r pair\, explicitly construct \nsuch pairs for infinitely many quadratic e
xtensions with odd class \nnumber\, and classify such characters of order
2.\n\nThis is a joint work with Zeev Rudnick.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yakov Varshavsky
DTSTART:20211026T173000Z
DTEND:20211026T183000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/23
DESCRIPTION:Title: The Hrushovski-Lang-Weil's estimates\nby Yakov Varshavsky as p
art of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nIn
the talk I am going to outline an algebro-geometric proof\nof Hrushovski's
generalization of the Lang-Weil estimates on the\nnumber of points in the
intersection of a correspondence with the\ngraph of Frobenius. This is a
joint work with K. V. Shuddhodan.\n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Papanikolas
DTSTART:20211207T183000Z
DTEND:20211207T193000Z
DTSTAMP:20260404T111006Z
UID:UNYONTC/24
DESCRIPTION:Title: Product formulas for periods of Drinfeld modules\nby Matt Papa
nikolas as part of Upstate New York Online Number Theory Colloquium\n\n\nA
bstract\nWe investigate new formulas for periods and quasi-periods of Drin
feld\nmodules\, similar to the product formula for the fundamental period
of the Carlitz\nmodule obtained through the Anderson-Thakur function. To t
hese ends we develop tools\nfor constructing rigid analytic trivialization
s for Drinfeld modules as infinite\nproducts of Frobenius twists of matric
es\, from which we recover the rigid analytic\ntrivialization given by Pel
larin in terms of Anderson generating functions. One\nparticular advantage
is that the terms of these infinite products can be determined\nfrom only
a finite amount of initial explicit calculation. Joint with C. Khaochim.\
n
LOCATION:https://stable.researchseminars.org/talk/UNYONTC/24/
END:VEVENT
END:VCALENDAR