A modular framework for generalized Hurwitz class numbers III

Andreas Mono

doi:10.1016/j.jmaa.2026.130398

paper

A modular framework for generalized Hurwitz class numbers III

arXiv:2504.17640 · doi:10.1016/j.jmaa.2026.130398

Abstract

In $2003$ , Pei and Wang introduced higher level analogs of the classical Cohen--Eisenstein series. In recent joint work with Beckwith, we found a weight $\frac{1}{2}$ sesquiharmonic preimage of their weight $\frac{3}{2}$ Eisenstein series under $ξ_{\frac{1}{2}}$ utilizing a construction from seminal work by Duke, Imamoglu and Tóth. In further joint work with Beckwith, when restricting to prime level, we realized our preimage as a regularized Siegel theta lift and evaluated its (regularized) Fourier coefficients explicitly. This relied crucially on work by Bruinier, Funke and Imamoglu. In this paper, we extend both works to higher weights. That is, we provide a harmonic preimage of Pei and Wang's generalized Cohen--Eisenstein series under $ξ_{\frac{3}{2} - k}$ , where $k > 1$ . Furthermore, when restricting to prime level, we realize them as outputs of a regularized Shintani theta lift of a higher level holomorphic Eisenstein series, which builds on recent work by Alfes and Schwagenscheidt. Lastly, we evaluate the regularized Millson theta lift of a higher level Maass--Eisenstein series, which is known to be connected to the Shintani theta lift by a differential equation by earlier work of Alfes and Schwagenscheidt.

accepted version, to be published in Journal of Mathematical Analysis and Applications

A modular framework for generalized Hurwitz class numbers III

Abstract

References in corpus (10)