A Novel Summation Formula for the Hurwitz-Kronecker Class Number
Yi-Ju Tsai
Published: 2025/9/10
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: $$ \sum_{t^2<p} H_w(t^2-p) = \frac{p-2}{3}. $$