Year: 2026
Type: article
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 sesquiharmonic preimage of their weight Eisenstein series under utilizing a construction from seminal work by Duke, Imamoḡlu 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 Imamoḡlu. 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 , where . 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.
Author: Andreas Mono
Institution: Vanderbilt University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4415307789