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SUMMARY:Akshaa Vatwani (Indian Institute of Technology Gandhinagar)
DTSTART:20220915T170000Z
DTEND:20220915T180000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/1/">Joint extreme values of $L$-functions</a>\nby Akshaa Vatwani (In
 dian Institute of Technology Gandhinagar) as part of CRG Weekly Seminars\n
 \n\nAbstract\nWe consider  $L$-functions $L_1\,\\ldots\,L_k$ from the Selb
 erg class having polynomial Euler product and satisfying Selberg's orthono
 rmality condition. We show that on every vertical line $s=\\sigma+it$ in t
 he complex plane with $\\sigma \\in(1/2\,1)$\, these $L$-functions simulta
 neously take "large" values inside a small neighborhood. \nOur method exte
 nds to $\\sigma=1$ unconditionally\, and to $\\sigma =1/2$ on the generali
 zed Riemann hypothesis. We also obtain similar joint omega results for arg
 uments of the given $L$-functions. \nThis is joint work with Kamalakshya M
 ahatab and Łukasz Pańkowski.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junxian Li (Mathematisches Institut der Universität Bonn)
DTSTART:20220922T170000Z
DTEND:20220922T180000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/2/">Joint value distribution of $L$-functions</a>\nby Junxian Li (Ma
 thematisches Institut der Universität Bonn) as part of CRG Weekly Seminar
 s\n\n\nAbstract\nIt is believed that distinct primitive $L$-functions are 
 “statistically independent”. The independence can be interpreted in ma
 ny different ways. We are interested in the joint value distributions and 
 their applications in moments and extreme values for distinct $L$-function
 s. We discuss some large deviation estimates in Selberg and Bombieri-Hejha
 l’s central limit theorem for values of several $L$-functions. On the cr
 itical line\, values of distinct primitive $L$-functions behave independen
 tly in a strong sense. However\, away from the critical line\, values of d
 istinct Dirichlet $L$-functions begin to exhibit some correlations.\n\nThi
 s is based on joint works with Shota Inoue.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youssef Sedrati (Institut Élie Cartan de Lorraine\, Nancy)
DTSTART:20220929T170000Z
DTEND:20220929T180000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/3/">Races of irreducible monic polynomials in function fields</a>\nb
 y Youssef Sedrati (Institut Élie Cartan de Lorraine\, Nancy) as part of C
 RG Weekly Seminars\n\n\nAbstract\nChebyshev noticed in 1853 that there is 
 a predominance\, for “most” real numbers $x ≥ 2$\, of the number of 
 primes $≤ x$ and congruent to $3$ modulo $4$ over primes $≤ x$ and con
 gruent to $1$ modulo $4$. Since then\, several generalizations of this phe
 nomenon have been studied\, notably in the case of prime number races with
  three or more competitors by Y. Lamzouri. In this talk\, I will present r
 esults related to the generalization of Y. Lamzouri’s work in the contex
 t of polynomial rings over finite fields. I will also discuss results conc
 erning races of irreducible monic polynomials involving two competitors. I
 n particular\, I will give examples where the races in the function field 
 setting behave differently than in the number field setting.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pranendu Darbar (The Norwegian University of Science and Technolog
 y)
DTSTART:20221006T170000Z
DTEND:20221006T180000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/4/">Multiplicative functions in short intervals</a>\nby Pranendu Dar
 bar (The Norwegian University of Science and Technology) as part of CRG We
 ekly Seminars\n\n\nAbstract\nIn this talk\, we are interested in a general
  class of multiplicative functions. For a function that belongs to this cl
 ass\, we will relate \nits “short average” to its “long average”. 
 More precisely\, we will compute the variance of such a function over shor
 t intervals by using Fourier analysis and by counting rational points on c
 ertain binary forms.\n\nThe discussion is applicable to some interesting m
 ultiplicative functions such as \n\\[\n\\mu_k(n)\, \\\, \\\,  \\frac{\\phi
 (n)}{n}\, \\\, \\\,  \\frac{n}{\\phi(n)}\, \\\, \\\, \\mu^2(n)\\frac{\\phi
 (n)}{n}\, \\\,\\\, \\sigma_{\\alpha}(n)\, \\\,\\\,\n (-1)^{\\#\\{p\\\,: \\
 \, p^k|n\\}}(n)\,\n\\]\nand many others and it provides various new result
 s and improvements to the previous result in the literature. This is a joi
 nt work with Mithun Kumar Das.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chung-Hang (Kevin) Kwan (University College London)
DTSTART:20221020T170000Z
DTEND:20221020T180000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/5/">Moments and Periods for $GL(3)$</a>\nby Chung-Hang (Kevin) Kwan 
 (University College London) as part of CRG Weekly Seminars\n\n\nAbstract\n
 In the past century\, the studies of moments of $L$-functions have been im
 portant in number\ntheory and are well-motivated by a variety of arithmeti
 c applications.\n\nThis talk will begin with two problems in elementary nu
 mber theory\, followed by a survey of\ntechniques in the past and the pres
 ent. We will slowly move towards the perspectives of period\nintegrals whi
 ch will be used to illustrate the interesting structures behind moments. I
 n particular\,\nwe shall focus on the “Motohashi phenomena”.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayla Gafni (University of Mississippi)
DTSTART:20221027T170000Z
DTEND:20221027T180000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/6/">Uniform distribution and geometric incidence theory</a>\nby Ayla
  Gafni (University of Mississippi) as part of CRG Weekly Seminars\n\n\nAbs
 tract\nThe Szemeredi-Trotter Incidence Theorem\, a central result in geome
 tric combinatorics\, bounds the number of incidences between n points and 
 m lines in the Euclidean plane. Replacing lines with circles leads to the 
 unit distance problem\, which asks how many pairs of points in a planar se
 t of n points can be at a unit distance. The unit distance problem breaks 
 down in dimensions $4$ and higher due to degenerate configurations that at
 tain the trivial bound. However\, nontrivial results are possible under ce
 rtain structural assumptions about the point set. In this talk\, we will g
 ive an overview of the history of these and other incidence results. Then 
 we will introduce a quantitative notion of uniform distribution and use th
 at property to obtain nontrivial bounds on unit distances and point-hyperp
 lane incidences in higher-dimensional Euclidean space. This is based on jo
 int work with Alex Iosevich and Emmett Wyman.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiannan Li (Kansas State University)
DTSTART:20221103T170000Z
DTEND:20221103T180000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/7/">Quadratic twists of modular $L$-functions</a>\nby Xiannan Li (Ka
 nsas State University) as part of CRG Weekly Seminars\n\n\nAbstract\nThe b
 ehavior of quadratic twists of modular $L$-functions at the critical point
  is related both to coefficients of half integer weight modular forms and 
 data on elliptic curves. Here we describe a proof of an asymptotic for the
  second moment of this family of $L$-functions\, previously available cond
 itionally on the Generalized Riemann Hypothesis by the work of Soundararaj
 an and Young. Our proof depends on deriving an optimal large sieve type bo
 und.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atul Dixit (Indian Institute of Technology Gandhinagar)
DTSTART:20221117T150000Z
DTEND:20221117T160000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/9/">Vorono$\\ddot{\\textrm{\\i}}$ summation formula for the generali
 zed divisor function $\\sigma_z^{(k)}(n)$</a>\nby Atul Dixit (Indian Insti
 tute of Technology Gandhinagar) as part of CRG Weekly Seminars\n\n\nAbstra
 ct\nFor a fixed $z\\in \\mathbb C$ and a fixed $k\\in \\mathbb N$\, let $\
 \sigma_z^{(k)}(n)$ denote the sum of $z$-th powers of those divisors $d$ o
 f $n$ whose $k$-th powers also divide $n$. This arithmetic function is a s
 imultaneous generalization of the well-known divisor function $\\sigma_z(n
 )$ as well as a divisor function $d^{(k)}(n)$ first studied by Wigert. A V
 orono$\\ddot{\\textrm{\\i}}$ summation formula is obtained for $\\sigma_z^
 {(k)}(n)$. An interesting thing to note here is that this arithmetic funct
 ion does not fall under the purview of the setting of the Hecke functional
  function with multiple gamma factors studied by Chandrasekharan and Naras
 imhan.  Some applications of the Vorono$\\ddot{\\textrm{\\i}}$ summation f
 ormula will be given. This is joint work with Bibekananda Maji and Akshaa 
 Vatwani.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sanoli Gun (The Institute of Mathematical Sciences)
DTSTART:20221124T180000Z
DTEND:20221124T190000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/10/">On non-Archimedean analogue of a question of Atkin and Serre</a
 >\nby Sanoli Gun (The Institute of Mathematical Sciences) as part of CRG W
 eekly Seminars\n\n\nAbstract\nLet $\\tau$ be the Ramanujan tau function.\n
 It is a well known question of Atkin and Serre that for any\n$\\epsilon > 
 0$\, there exists a constant $c(\\epsilon) >0$\nsuch that $|\\tau(p)| \\ge
  c(\\epsilon) p^{(k-3)/2 - \\epsilon}$.\nIn this talk\, we will address a 
 non-Archimedean\nanalogue of this question which improves the recent\nboun
 d of Bennett\, Gherga\, Patel and Siksek.\nThis is a report on a joint wor
 k with Yuri Bilu and Sunil Naik.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anurag Sahay (University of Rochester)
DTSTART:20221201T180000Z
DTEND:20221201T190000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/11/">The value distribution of the Hurwitz zeta function with an irr
 ational shift</a>\nby Anurag Sahay (University of Rochester) as part of CR
 G Weekly Seminars\n\n\nAbstract\nThe Hurwitz zeta function $\\zeta(s\,\\al
 pha)$ is a shifted integer analogue of the Riemann zeta function which sha
 res many of its properties\, but is not an "$L$-function" under any reason
 able definition of the word. We will first review the basics of the value 
 distribution of the Riemann zeta function in the critical strip (moments\,
  Bohr--Jessen theory...) and then contrast it with the value distribution 
 of the Hurwitz zeta function.\n\nOur focus will be on shift parameters $\\
 alpha \\notin \\mathbb{Q}$\, i.e.\, algebraic irrational or transcendental
 . We will present a new result (joint with Winston Heap) on moments of the
 se objects on the critical line.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shashank Chorge (University of Rochester)
DTSTART:20221013T170000Z
DTEND:20221013T180000Z
DTSTAMP:20260404T095031Z
UID:crgseminar/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/crgse
 minar/12/">Extreme values of the Riemann zeta and Dirichlet $L$-functions 
 at critical points</a>\nby Shashank Chorge (University of Rochester) as pa
 rt of CRG Weekly Seminars\n\n\nAbstract\nWe compute extreme values of the 
 Riemann zeta function at the critical\npoints of the zeta function in the 
 critical strip. i.e. the points where $\\zeta'(s) = 0$ and $\\Re s < 1$. W
 e show that the values taken by the zeta function at these points\nare ver
 y similar to the extreme values taken without any restrictions. We will\ns
 how geometric significance of such points.\n\nWe also compute extreme valu
 es of Dirichlet $L$-functions at the critical points of the zeta function 
 to the right of $\\Re s = 1$. It shows statistical independence of $L$-fun
 ctions and zeta function in a certain way as these values are very similar
  to the values taken by $L$-functions without any restriction.\n
LOCATION:https://stable.researchseminars.org/talk/crgseminar/12/
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