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Washington State University

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics and Statistics

Neill Hall 5W

April 23, Monday, 4:10 - 5:00 PM

Shenhui Liu

Department of Mathematics

University of Toronto

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics and Statistics

Neill Hall 5W

April 23, Monday, 4:10 - 5:00 PM

Shenhui Liu

Department of Mathematics

University of Toronto

Title: Nonvanishing of L-functions

Abstract: L-functions are important and interesting analytic objects in number theory. The special values of L-functions and their derivatives at the central point of the critical strip are connected with several branches of mathematics. In this talk, we will focus the nonvanishing of such values and will explain how to use the method of moments and the mollification method to obtain strong nonvanishing results for L-functions in various families of automorphic forms. If time permits, we will mention some applications of the nonvanishing results.

Abstract: L-functions are important and interesting analytic objects in number theory. The special values of L-functions and their derivatives at the central point of the critical strip are connected with several branches of mathematics. In this talk, we will focus the nonvanishing of such values and will explain how to use the method of moments and the mollification method to obtain strong nonvanishing results for L-functions in various families of automorphic forms. If time permits, we will mention some applications of the nonvanishing results.