2024/03/26 by Olivia Beckwith, Beckwith, Olivia, Andreas Mono +1
Computer Science · Environmental Science · Mathematics · #11F12 #11F30 (Secondary) #11F37 (Primary) #FOS: Mathematics #Number Theory (math.NT) #Research studies in Vietnam #Rings, Modules, and Algebras #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2403.17829
openalex publication_date 2024/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discover a non-trivial relation between the mock modular generating functions of the level 1 and level N Hurwitz class numbers. This relation yields a holomorphic modular form of weight (3)/(2) and level 4N, where N > 1 is stipulated to be odd and square-free. We extend this observation to a non-holomorphic framework and obtain a higher level non-holomorphic Zagier Eisenstein series as well as a preimage G of it under the differential operator ξ(1)/(2). All of these observations are deduced from a more general inspection of a certain weight (1)/(2) Maass--Eisenstein series of level 4N at its spectral point s=(3)/(4). This idea goes back to Duke, Imamoglu and Tóth in level 4 and relies on the theory of so-called sesquiharmonic Maass forms. We calculate the Fourier expansion of G and ξ(1)/(2)G. We conclude by offering examples if N=5 or N=7 as well as some questions for future work.