Number Theory Seminar: 3 Talks

This seminar is aimed at scientists in general, not only to mathematicians.

10:00-10:45
Title: Multiple zeta functions associated with 2-colored rooted trees
Speaker: Dr. Masataka Ono (Keio University)
Abstract: In our recent work, we introduced a combinatorial object and finite sum associated with them which we call finite multiple zeta values associated with 2-colored rooted trees and gave a unified interpretation to some types of finite multiple zeta values. In this talk, we introduce multiple zeta function associated with 2-colored rooted tree and discuss its analytic properties, for example, the possible singularities and functional equations.

10:55-11:40
Title: Modular forms and trace formulas with applications to equidistributions of their Fourier coefficients
Speaker: Dr. Shingo Sugiyama (Nihon University)
Abstract: Modular forms are interesting objects in number theory as they are related to arithmetic problems. Trace formulas of Hecke operators acting on modular forms are very useful tools to study arithmetic invariants: Fourier coefficients, special values of L-functions, Hurwitz class numbers. We will start fundamental notions on modular forms and trace formulas of Hecke operators for non-experts, and introduce our results on a generalization of Serre’s vertical Sato-Tate law. Some results in this talk are based on a joint work with Masao Tsuzuki (Sophia University).

11:50-12:35
Title: On a generalization of Dobinski's formula
Speaker: Yoshinosuke Hirakawa (Keio University)
Abstract: Dobinski's formula is a very classical formula, which expresses the Bell number as an infinite series. Here, the Bell number is the number of partitions of a finite set. Such a "combinatorial-analytic" formula should lead us to more beautiful number theory. In this talk, we introduce a generalization of Dobinski's formula by means of a certain multiple generalization of the exponential function.