# Moments of $L$-functions Workshop

Establishing asymptotic formulas for moments of L-functions has been a main goal of analytic number theory for over a century. This topic is strongly connected to the generalized Lindel of Hypothesis and various non-vanishing conjectures, and it has witnessed substantial progress in the last three decades. This one-week workshop brings together established and early-career researchers with expertise and interest in moments and zeros of L-functions to discuss various aspects of the cur-
rent research, with special emphasis on multiple Dirichlet series, shifted convolution sums, random matrix theory, and spectral theory of automorphic forms. The purpose of this event is to highlight the recent advances in this area and initiate discussions and collaborations among researchers across the different sub-disciplines of this field. In particular, we are interested in exploring connections between the multiple Dirichlet series approach and the approximate functional equation approach to studying moments of L-functions, perhaps opening up new ways to understanding some of these moments. This event aims to provide a collaborative and supportive research environment for young researchers and an opportunity for established researchers to mentor and exchange ideas.

This event is part of the PIMS Collaborative Research Group L-Functions in Analytic Number Theory.

Title Speaker Date
Moments of the Hurwitz zeta function Anurag Sahay July 29, 2022 - 3:30pm
An extension of Venkatesh's converse theorem to the Selberg class Min Lee July 29, 2022 - 2:00pm
Averages of long Dirichlet polynomials with modular coefficients Alessandro Fazzari July 29, 2022 - 1:30pm
Local statistics for zeros of Artin--Schreier $L$-functions Alexei Entin July 29, 2022 - 11:00am
Moments of $L$-functions in the world of number field counting Brandon Alberts July 29, 2022 - 10:30am
The eighth moment of the Riemann zeta function Quanli Shen July 29, 2022 - 9:00am
Geodesic restrictions of Maass forms and moments of Hecke $L$-functions Peter Humphries July 28, 2022 - 3:30pm
Twisted first moment of $GL(3)\times GL(2)$ $L$-function Jakob Streipel July 28, 2022 - 2:30pm
Moments and periods for $GL(3)$ Chung-Hang Kwan July 28, 2022 - 2:00pm
Double square moments and bounds for resonance sums for cusp forms Praneel Samanta July 28, 2022 - 1:30pm
$L^p$-norm bounds for automorphic forms Rizwanur Khan July 28, 2022 - 9:00am
Moments of large families of Dirichlet $L$-functions Vorrapan Chandee July 27, 2022 - 11:00am
Discrete Moments Fatma Cicek July 27, 2022 - 10:30am
Limitations to equidistribution in arithmetic progressions Aditi Savalia July 27, 2022 - 9:30am
Quantum variance for automorphic forms Bingrong Huang, July 27, 2022 - 9:00am
Logging of the zeta-function, but only for a few moments! Tim Trudgian July 26, 2022 - 3:30pm
The third moment of quadratic $L$-Functions Ian Whitehead July 26, 2022 - 2:00pm
Asymptotic mean square of product of higher derivatives of the zeta-function and Dirichlet polynomials Mithun Das July 26, 2022 - 9:30am
Lambert series of logarithm and a mean value theorem for $\zeta(\frac{1}{2}-it)\zeta'(\frac{1}{2}+it)$ Atul Dixit July 26, 2022 - 9:00am
Negative moments of the Riemann zeta function Alexandra Florea July 25, 2022 - 3:30pm
The recipe for moments of $L$-functions Siegfried Baluyot July 25, 2022 - 2:00pm
The generalised Shanks's conjecture Andrew Pearce-Crump July 25, 2022 - 1:30pm
One-level density of zeros of Dirichlet L-functions over function fields Hua Lin July 25, 2022 - 11:30am
Distributions of sums of the divisor function over function fields Matilde Lalín July 25, 2022 - 10:30am
Selberg's central limit theorem for quadratic Dirichlet $L$-functions over function fields Allysa Lumley July 25, 2022 - 9:30am