Zhiyu Zhang

Affiliation: Stanford University

Title Of Talk: Modularity of arithmetic theta series over finite fields

Abstract: Special families of abelian varieties over finite fields occur naturally in different contexts. Consider such a special family over a projective line, from Shimura curves with Drinfeld uniformization. As in the Kudla program, one may count the number of elements in this family with extra symmetry, and form an arithmetic analog of theta series. Our main result is that such a counting series is indeed a modular form. Then I will discuss some arithmetic applications of modularity.

WARNING: This page contains MATH-JAX

Last update made Tue Mar 10 21:28:06 CDT 2026.
Please report problems to: fgarvan@ufl.edu