Averages and moments associated to class numbers of imaginary quadratic fields

Abstract

For any odd prime $\ell$, let $h_{\ell }(-d)$ denote the $\ell$-part of the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-d})$. Nontrivial pointwise upper bounds are known only for $\ell =3$; nontrivial upper bounds for averages of $h_{\ell }(-d)$ have previously been known only for $\ell =3,5$. In this paper we prove nontrivial upper bounds for the average of $h_{\ell }(-d)$ for all primes $\ell \ge 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\ell \ge 3$.

26 pages; minor edits to exposition and notation, to agree with published version

References in corpus (1)

• On the Davenport-Heilbronn theorems and second order terms

Cited by in corpus (1)

• Bounds for the $\ell$-torsion in class groups