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arXiv · 2509.08281

A Novel Summation Formula for the Hurwitz-Kronecker Class Number

Yi-Ju Tsai
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Abstract

The purpose of this paper is to present a novel and elegant summation formula for $H_w$, the Kronecker-Hurwitz class number. Specifically, for any prime $p$, we have the formula: $$ \sum_{t^2<p} H_w(t^2-p) = \frac{p-2}{3}. $$

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Yi-Ju Tsai. 2025-09-10. A Novel Summation Formula for the Hurwitz-Kronecker Class Number. https://arxiv.org/abs/2509.08281

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