Work

Hurwitz class number relations and mock modular forms

Year: 2026

Type: preprint

Abstract: A classical class number relation of Hurwitz expresses the Fourier coefficients of the product of a unary theta function and the class number generating function. Here, we establish an infinite family of analogous class number relations obtained by replacing the unary quadratic form $m^2$ by positive-definite binary quadratic forms. These identities involve Cohen's generalized class numbers and depend only on the genus of the underlying quadratic form. For this, we construct a genus-dependent level-lowering operator.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.14371

Authors: Bringmann, Kathrin, Guo, Jia-Wei, Kane, Ben, Mertens, Michael, Yang, Yifan

Institutions: TH Köln - University of Applied Sciences, University of Cologne

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: European Commission

OpenAlex ID: W7203595885

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