Olivia.Beckwith

Affiliation: Tulane University

Title Of Talk: A modular framework for generalized Hurwitz class numbers

Abstract: We explore the modular properties of generating functions for Hurwitz class numbers endowed with level structure. Our work is based on an inspection of the weight 1/2 Maass–Eisenstein series of level 4N at its spectral point s=3/4, extending the work of Duke, Imamo?lu and Tóth in the level 4N setting. We construct a higher level analogue of Zagier’s level 4 mock modular Eisenstein series and a preimage under the -operator. We explore linear relations among this series, Zagier’s Eisenstein series, and higher level holomorphic Eisenstein series defined by Pei and Wang, as well as connections to ternary quadratic forms. Furthermore, we connect the aforementioned results to a regularized Siegel theta lift as well as a regularized Kudla–Millson theta lift for odd prime levels, which builds on earlier work by Bruinier, Funke and Imamo?lu. This is joint work with Andreas Mono and Ngoc Trinh Le.

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