Self-Correlations of Hurwitz Class Numbers
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 Σn < X H(n) H(n+) for fixed ∈ Z, in which H(n) denotes the Hurwitz class number.
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