講演者:  Asif Zaman  (University of Toronto)

タイトル:  Effective Brauer-Siegel theorems for Artin L-functions

講演者:  小野塚 友一（大分大学）

タイトル:  Distribution of a-points of Symmetric Sums of Multiple Zeta Functions

講演者:  井上 翔太（日本大学）

タイトル:  Discrepancy estimate of the Riemann zeta-function on the critical line

アブストラクト:  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.

講演者:  Roma Kačinskaitė  (Vilnius University)

タイトル:  Classes of zeta-functions: problems on value-distribution and universality

講演者:  村原 英樹（北九州市立大学）

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

アブストラクト:  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. 

講演者:  Łukasz Pańkowski  (Adam Mickiewicz University) 

タイトル:  On universality of the Riemann zeta-function in short intervals

講演者:  梅垣 由美子（奈良女子大学）

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

アブストラクト:  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. 

講演者:  峰 正博（早稲田大学） 

タイトル:  Joint value-distributions of symmetric power L-functions in the level aspect

アブストラクト:  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. 

講演者:  Naomi Tanabe  (Bowdoin College)

タイトル:  Moments of L-functions

アブストラクト:  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. 

講演者:  小林 弘京（水産大学校）

タイトル:  On the distribution of the zeros of generalized Hardy Z-functions and their derivatives