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BEGIN:VEVENT
SUMMARY:Alexandre de Faveri (Stanford University)
DTSTART:20250114T210000Z
DTEND:20250114T220000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/1/">Non-vanishing for cubic Hecke $L$-functions</a>\nby Alexandre
  de Faveri (Stanford University) as part of CRG Weekly Seminars\n\n\nAbstr
 act\nI will discuss recent work with Chantal David\, Alexander Dunn\, and 
 Joshua Stucky\, in which we prove that a positive proportion of Hecke $L$-
 functions associated to the cubic residue symbol modulo square-free Eisens
 tein integers do not vanish at the central point. Our principal new contri
 bution is the asymptotic evaluation of the mollified second moment. No suc
 h asymptotic formula was previously known for a cubic family (even over fu
 nction fields). \n\nOur new approach makes crucial use of Patterson's eval
 uation of the Fourier coefficients of the cubic metaplectic theta function
 \, Heath-Brown's cubic large sieve\, and a Lindelöf-on-average upper boun
 d for the second moment of cubic Dirichlet series that we establish. The s
 ignificance of our result is that the family considered does not satisfy a
  perfectly orthogonal large sieve bound. This is quite unlike other famili
 es of Dirichlet $L$-functions for which unconditional results are known (n
 amely the family of quadratic characters and the family of all Dirichlet c
 haracters modulo q). Consequently\, our proof has fundamentally different 
 features from the corresponding works of Soundararajan and of Iwaniec and 
 Sarnak.\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Carneiro (ICTP (International Centre for Theoretical Physi
 cs))
DTSTART:20250121T180000Z
DTEND:20250121T190000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/2/">Effective equidistribution of Galois orbits for mildly regula
 r test functions</a>\nby Emanuel Carneiro (ICTP (International Centre for 
 Theoretical Physics)) as part of CRG Weekly Seminars\n\n\nAbstract\nWe pro
 vide a detailed study on effective versions of the celebrated Bilu's equid
 istribution theorem for Galois orbits of sequences of points of small heig
 ht in the $N$-dimensional algebraic torus\, identifying the qualitative de
 pendence of the convergence in terms of the regularity of the test functio
 ns considered. We develop a general Fourier analysis framework that extend
 s previous results obtained by Petsche (2005)\, and by D'Andrea\, Narváez
 -Clauss and Sombra (2017). This is a joint work with Mithun Das (ICTP).\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kim Klinger Logan (Kansas State University)
DTSTART:20250128T210000Z
DTEND:20250128T220000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/3/">Convolution Sums from Trace Formulae</a>\nby Kim Klinger Loga
 n (Kansas State University) as part of CRG Weekly Seminars\n\n\nAbstract\n
 Previously we found certain convolution sums of divisor functions arising 
 from physics yield Fourier coefficients of modular forms. In this talk we 
 will discuss the limitations of the current proof of these formulas. We wi
 ll also explore the connection with the Petersson and Kuznetsov Trace Form
 ulae and the possibility of extending these formulas to other cases. The w
 ork mentioned in this talk is in collaboration with Ksenia Fedosova\, Step
 hen D. Miller\, Danylo Radchenko\, and Don Zagier.\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sun Kai (Ken) Leung (Université de Montréal)
DTSTART:20250304T210000Z
DTEND:20250304T220000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/5/">Higher-order Titchmarsh problem via exceptional zeros</a>\nby
  Sun Kai (Ken) Leung (Université de Montréal) as part of CRG Weekly Semi
 nars\n\n\nAbstract\nThe higher-order Titchmarsh problem concerns the corre
 lation between higher divisor functions and primes. In this talk\, I will 
 explain how to derive an asymptotic formula for this correlation in approp
 riate ranges\, assuming the existence of a "strong" Landau-Siegel zero. If
  time permits\, I will also briefly discuss my ongoing work on further ill
 usory consequences.\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Besfort Shala (University of Bristol)
DTSTART:20250311T200000Z
DTEND:20250311T210000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/6/">Almost sure bounds for sums of random multiplicative function
 s</a>\nby Besfort Shala (University of Bristol) as part of CRG Weekly Semi
 nars\n\n\nAbstract\nI will start with a survey on sums of random multiplic
 ative functions\, focusing on distributional questions and almost sure upp
 er bounds and $\\Omega$-results. In this context\, I will describe previou
 s work with Jake Chinis on a central limit theorem for correlations of Rad
 emacher multiplicative functions\, as well as ongoing work on establishing
  almost sure sharp bounds for them.\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Frolenkov (HSE University)
DTSTART:20250204T180000Z
DTEND:20250204T190000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/7/">Moments of symmetric square $L$-functions</a>\nby Dmitry Frol
 enkov (HSE University) as part of CRG Weekly Seminars\n\n\nAbstract\nI am 
 going to discuss various results on moments of symmetric square $L$-functi
 ons and some of their applications.  I will mainly focus on a recent resu
 lt of R. Khan and M. Young and our improvement of it. Khan and Young prove
 d a mean Lindelöf estimate for the second moment of Maass form symmetric-
 square $L$-functions $L(\\textrm{sym}^2 u_{j}\,1/2+it)$  on the short int
 erval of length $G\\gg |t_j|^{1+\\epsilon}/t^{2/3}$\, where $t_j$ is a spe
 ctral parameter of the corresponding Maass form. Their estimate yields a s
 ubconvexity estimate for $L(\\textrm{sym}^2 u_{j}\,1/2+it)$ as long as $|t
 _j|^{6/7+\\delta}\\ll t<(2-\\delta)|t_j|$. We  obtain a mean Lindelöf e
 stimate for the same moment in shorter intervals\, namely for $G\\gg |t_j|
 ^{1+\\epsilon}/t$. As a corollary\, we prove a subconvexity estimate for $
 L(\\textrm{sym}^2 u_{j}\,1/2+it)$  on the interval $|t_j|^{2/3+\\delta}\\
 ll t\\ll |t_j|^{6/7-\\delta}$. This is joint work with Olga Balkanova.\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sumaia Saad Eddin (RICAM (Johann Radon Institute for Computational
  and Applied Mathematics))
DTSTART:20250325T170000Z
DTEND:20250325T180000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/8/">A Survey on the Evaluation of Dirichlet $L$-Functions and The
 ir Logarithmic Derivatives on the Line $\\Re (s)=1$</a>\nby Sumaia Saad Ed
 din (RICAM (Johann Radon Institute for Computational and Applied Mathemati
 cs)) as part of CRG Weekly Seminars\n\n\nAbstract\nThe values of Dirichlet
  $L$-functions at $s = 1$ have long attracted considerable attention due t
 o their deep algebraic and geometric significance. In contrast\, the logar
 ithmic derivatives of Dirichlet $L$-functions at $s = 1$\, which play a ke
 y role in the study of prime distribution\, remain less thoroughly underst
 ood despite their importance\, a topic of interest since Dirichlet's groun
 dbreaking work in 1837.\n\nIn this talk\, we survey known results on the e
 valuation of Dirichlet $L$-functions and their logarithmic derivatives at 
 $s = 1 + i t_0$\, for a fixed real number $t_0$.\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arshay Sheth (University of Warwick)
DTSTART:20250225T210000Z
DTEND:20250225T220000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/9/">Euler products inside the critical strip</a>\nby Arshay Sheth
  (University of Warwick) as part of CRG Weekly Seminars\n\n\nAbstract\nEve
 n though Euler products of $L$-functions are generally valid only to the r
 ight of the critical strip\, there is a strong sense in which they should 
 persist even inside the critical strip. Indeed\, the behaviour of Euler pr
 oducts inside the critical strip is very closely related to several major 
 problems in number theory including the Riemann Hypothesis and the Birch a
 nd Swinnerton-Dyer conjecture. In this talk\, we will give an introduction
  to this topic and then discuss recent work on establishing asymptotics fo
 r partial Euler products of $L$-functions in the critical strip. We will e
 nd by giving applications of these results to questions related to Chebysh
 ev's bias.\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Pedro Ramos (SISSA (Scuola Internazionale Superiore di Stu
 di Avanzati))
DTSTART:20250401T170000Z
DTEND:20250401T180000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/10/">Zeros of $L$-functions in low-lying intervals and de Branges
  spaces</a>\nby Antonio Pedro Ramos (SISSA (Scuola Internazionale Superior
 e di Studi Avanzati)) as part of CRG Weekly Seminars\n\n\nAbstract\nWe con
 sider a variant of a problem first introduced by Hughes and Rudnick (2003)
  and generalized by Bernard (2015) concerning conditional bounds for small
  first zeros in a family of $L$-functions. Here we seek to estimate the si
 ze of the smallest intervals centered at a low-lying height for which we c
 an guarantee the existence of a zero in a family of $L$-functions. This le
 ads us to consider an extremal problem in analysis which we address by app
 lying the framework of de Branges spaces\, introduced in this context by C
 arneiro\, Chirre\, and Milinovich (2022).\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kübra Benli
DTSTART:20250318T200000Z
DTEND:20250318T210000Z
DTSTAMP:20260422T225920Z
UID:crgseminarwinter2025/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/crgseminarwi
 nter2025/11/">Explicit Deuring-Heilbronn phenomenon for Dirichlet $L$-func
 tions</a>\nby Kübra Benli as part of CRG Weekly Seminars\n\n\nAbstract\nD
 euring-Heilbronnn phenomenon\, quantitatively established by Linnik in 194
 4\, describes how the existence of a Landau-Siegel zero\, which is real an
 d near $s=1$\, affects the location of the rest of the zeros of the Dirich
 let $L$-functions to the same modulus. In this talk\, we discuss an explic
 it version of this phenomenon based on our work initiated in the summer sc
 hool "Inclusive Paths in Explicit Number Theory" with Asif Zaman\, Shivani
  Goel\, and Henry Twiss.\n
LOCATION:https://researchseminars.org/talk/crgseminarwinter2025/11/
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