Speaker:  Asif Zaman  (University of Toronto)

Title:  Effective Brauer-Siegel theorems for Artin L-functions

Speaker:  Tomokazu Onozuka  (Oita University)

Title:  Distribution of a-points of Symmetric Sums of Multiple Zeta Functions

Speaker:  Shota Inoue  (Nihon University)

Title:  Discrepancy estimate of the Riemann zeta-function on the critical line

Abstract:  In 1912, Bohr and Courant proved that the values of the Riemann zeta function are dense in the complex plane along any vertical line whose real part lies between 1/2 and 1. For vertical lines with real part different from 1/2 (i.e., lines other than the critical line), the question of the denseness has been completely resolved, although in some cases the Riemann Hypothesis is required. However, the density on the critical line itself remains an open problem. In this talk, we consider a discrepancy estimate for Selberg’s central limit theorem on the critical line, in connection with this open problem. Our estimate improves upon Selberg’s original bound. We will also explain that our method yields a proof of the denseness under assumptions such as the pair correlation conjecture and a certain independence hypothesis between zeros and primes.

Speaker:  Roma Kačinskaitė  (Vilnius University)

Title:  Classes of zeta-functions: problems on value-distribution and universality

Speaker:  Hideki Murahara  (The University of Kitakyushu)

Title:  Asymptotic behavior of multiple zeta functions at non-positive integer points and generalized Gregory coefficients

Abstract:  Due to their singularities, multiple zeta functions behave sensitively at non-positive integer points. In this talk, we first give a result on the asymptotic behavior of the Hurwitz-Lerch multiple zeta functions near non-positive integer points by using the Apostol-Bernoulli polynomials. From this result, we can evaluate limit values at these points.
Following this, we focus on the asymptotic behavior at the origin (0,…,0) and unveil the generating series of the asymptotic coefficients as a generalization of the classical Gregory coefficients. This enables us to reveal the underlying symmetry of the asymptotic coefficients. Additionally, we extend the relationship between the asymptotic coefficients and the Gregory coefficients to include Hurwitz multiple zeta functions.
The first part of this talk is based on joint work with Tomokazu Onozuka (Oita University). The second part is joint work with Toshiki Matsusaka (Kyushu University) and Tomokazu Onozuka. 

Speaker:  Łukasz Pańkowski  (Adam Mickiewicz University) 

Title:  On universality of the Riemann zeta-function in short intervals

Speaker:  Yumiko Umegaki  (Nara Women's University)

Title:  On M-functions related to the values of logarithms of Dirichlet L-functions in the modulus aspect

Abstract:  In 2008, Ihara constructed the M-function which is the density function of the values of logarithmic derivatives of Dirichlet L-functions. In 2011, Ihara and Matsumoto obtained several M-functions for the values of logarithms or the values of logarithmic derivatives of L-functions. They focused on the L-functions with a similar type of Euler product to Riemann zeta function or Dirichlet L-function. Since then, M-functions for various L-functions have attracted interest. In this talk, I will show the M-functions for logarithms of the absolute values of Dirichlet L-functions and the values of logarithms of Dirichlet L-functions associated with real characters. This is a joint work with Manami Hosoi. 

Speaker:  Masahiro Mine  (Waseda University)

Title:  Joint value-distributions of symmetric power L-functions in the level aspect

Abstract:  The distribution of the values of automorphic L-functions L(s,f) when the cusp form f varies while fixing s has been studied by many researchers. For example, Cogdell and Michel studied the value-distributions of symmetric power L-functions by using a random model for the Satake parameters. In this talk, we consider the distribution of pairs of the values for two symmetric power L-functions in the level aspect. As an application, we obtain a joint denseness result for the values of symmetric power L-functions, which implies that they behave “independently” in a sense. 

Speaker:  Naomi Tanabe  (Bowdoin College)

Title:  Moments of L-functions

Abstract:  Moments of L-functions provide a powerful tool for understanding the distribution of the values of L-functions, particularly on the critical line. They capture subtle information about the size and zeros of L-values that lies beyond the reach of individual estimates. In this talk, I will survey key developments in the moment problem for various L-functions and then focus on ongoing joint work with Alia Hamieh, which aims to establish an asymptotic for the second moments of L-functions attached to modular forms. 

Speaker:  Hirotaka Kobayashi  (National Fisheries University)

Title:  On the distribution of the zeros of generalized Hardy Z-functions and their derivatives