Self-Correlations of Hurwitz Class Numbers
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911223927275520 |
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| author | Walker, Alexander |
| author_facet | Walker, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-Correlations of Hurwitz Class Numbers Walker, Alexander Number Theory 11Mxx 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. |
| title | Self-Correlations of Hurwitz Class Numbers |
| topic | Number Theory 11Mxx |
| url | https://arxiv.org/abs/2402.01455 |