Self-correlations of Hurwitz class numbers

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 P n<X H .n/H .nC `/ for fixed `2 , in which H .n/ denotes the Hurwitz class number.