The moments and statistical distribution of class numbers of quadratic fields with prime discriminant (Q392995)

The author generalizes classical asymptotic formulas of Gauss, Lipschitz and Siegel on class numbers of quadratic fields. Let \(h(d)\) the class number and \(\varepsilon(d)\) the fundamental unit of \(\mathbb{Q}(\sqrt{d})\). If the discriminant \(d\) is a prime \(p\), he finds asymptotic formulae of the moments \[ \sum_{p\leq x,p\equiv 3\,\text{mod}\,4} h(-p)^k\quad\text{ and }\sum_{p\leq x,p\equiv 1\,\text{mod}\,4} (h(p)\log\varepsilon(p))^k. \] He further studies the statistical distribution of these class numbers, introducing a certain random Euler product.