2024/11/12 by Olivia Beckwith, Beckwith, Olivia, Andreas Mono +1 · 1 citation
Computer Science · Mathematics · #11F12 #11F27 #11F30 (Secondary) #11F37 (Primary) #FOS: Mathematics #Holomorphic and Operator Theory #Number Theory (math.NT) #Polynomial and algebraic computation #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2411.07962
openalex publication_date 2024/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent preprint, we constructed a sesquiharmonic Maass form G of weight (1)/(2) and level 4N with N odd and squarefree. Extending seminal work by Duke, Imamoglu, and Tóth, G maps to Zagier's non-holomorphic Eisenstein series and a linear combination of Pei and Wang's generalized Cohen--Eisenstein series under the Bruinier--Funke operator ξ(1)/(2). In this paper, we realize G as the output of a regularized Siegel theta lift of 1 whenever N=p is an odd prime building on more general work by Bruinier, Funke and Imamoglu. In addition, we supply the computation of the square-indexed Fourier coefficients of G. This yields explicit identities between the Fourier coefficients of G and all quadratic traces of 1. Furthermore, we evaluate the Millson theta lift of 1 and consider spectral deformations of 1.