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arXiv · 2608.14371

Hurwitz class number relations and mock modular forms

Kathrin Bringmann·Jia-Wei Guo·Ben Kane·Michael Mertens·Yifan Yang
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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.

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Kathrin Bringmann, Jia-Wei Guo, Ben Kane, Michael Mertens, Yifan Yang. 2026-08-14. Hurwitz class number relations and mock modular forms. https://arxiv.org/abs/2608.14371

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