Low-lying zeros of symmetric power L-functions weighted by L-values

Abstract: There is a philosophy due to Katz and Sarnak that low-lying zeros of a family of L-functions should be distributed with a density function coming from random matrix theory. This has been supported by several evidences on Dirichlet L-functions, standard L-functions attached to elliptic modular forms, and so on. In this talk, we discuss low-lying zeros of symmetric power L-functions attached to Hilbert modular forms, weighted by special values of symmetric square L-functions. We also suggest a conjecture on relations between low-lying zeros and special values of L-functions from our result.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October