Number Theory Seminar

Date: April 23, 2024

Time: 09:45AM - 10:45AM

Location: BLOC 302

Speaker: Shifan Zhao, The Ohio State University

Title: Low-lying zeros of L-functions attached to Siegel modular forms

Abstract: The Katz-Sarnak heuristic predicts that the distribution of low-lying zeros of families of automorphic L-functions are governed by certain classical compact groups determined by the family. In this talk I will present some recent progress concerning low-lying zeros of spinor and standard L-functions of Siegel modular forms. I will first describe these results in the $k$ (weight) aspect, and then explain how to extend the support of Fourier transforms of test functions by averaging over $k$. I will also discuss applications towards the non-vanishing of central L-values.