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arXiv · 2402.01455

Self-Correlations of Hurwitz Class Numbers

Alexander Walker
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Abstract

The asymptotic study of class numbers of binary quadratic forms is a foundational problem in arithmetic statistics. Here, we investigate finer statistics of class numbers by studying their self-correlations under additive shifts. Specifically, we produce uniform asymptotics for the shifted convolution sum $\sum_{n < X} H(n) H(n+\ell)$ for fixed $\ell \in \mathbb{Z}$, in which $H(n)$ denotes the Hurwitz class number.

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Alexander Walker. 2024-02-02. Self-Correlations of Hurwitz Class Numbers. https://doi.org/10.2140/ant.2025.19.2433

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