Theta Series for Quadratic Forms of Signature (n-1,1) with (Spherical) Polynomials II

2022/01/11 by Christina Roehrig, Roehrig, Christina, Sander Zwegers +1
Mathematics · #11F11 #11F12 #11F27 #11F37 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.03986

openalex publication_date 2022/01/11 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We generalize the construction from arXiv:2102.09329 of theta series for quadratic forms of signature (n-1,1) with homogeneous and spherical polynomials. Namely, we allow that the parameters c₁,c₂, which define the theta series and ensure the convergence of the defining series, are located on the boundary of the cone C_Q. This enables us to study several interesting examples such as Eisenstein series, modular forms on Γ₀(4) which appear during the investigation of quadratic polynomials of a fixed discriminant, and a mock theta function of order 2 that is connected to the generating function of the Hurwitz class numbers H(8n+7).

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