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arXiv · 1409.3177

Averages and moments associated to class numbers of imaginary quadratic fields

D. R. Heath-Brown·L. B. Pierce
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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 $\ell \geq 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\ell \geq 3$.

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D. R. Heath-Brown, L. B. Pierce. 2014-09-10. Averages and moments associated to class numbers of imaginary quadratic fields. https://arxiv.org/abs/1409.3177

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