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

2021/02/18 by Christina Roehrig, Roehrig, Christina, Sander Zwegers +1 · 1 citation
Mathematics · #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.2102.09329

openalex publication_date 2021/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct almost holomorphic and holomorphic modular forms by considering\ntheta series for quadratic forms of signature (n-1,1). We include homogeneous\nand spherical polynomials in the definition of the theta series (generalizing a\nconstruction of the second author) to obtain holomorphic, almost holomorphic\nand modular theta series. We give a criterion for these series to coincide,\nenabling us to construct almost holomorphic and holomorphic cusp forms on\ncongruence subgroups of the modular group. Further, we provide numerous\nexplicit examples.\n

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