Abstract

In this talk, we consider Hurwitz class numbers related to imaginary quadratic fields. Using a result of Zagier, the generating function for these class numbers is a mock modular form, and the product of this mock modular form with a unary theta function is a special class of functions known as mixed-mock modular forms. Such products naturally occur when investigating distributions of traces of Frobenius for elliptic curves over finite fields. Using the theory of harmonic Maass forms and holomorphic projection, we investigate such distributions when the trace of Frobenius is restricted to a fixed arithmetic progression. This is based on joint work with Kathrin Bringmann and Sudhir Pujahari.

 

Organizer: Yifan Yang (NTU)