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Self-Correlations of Hurwitz Class Numbers
- Publication Year :
- 2024
-
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.<br />Comment: 41 pages, 0 figures
- Subjects :
- Mathematics - Number Theory
11Mxx
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2402.01455
- Document Type :
- Working Paper