Averages and moments associated to class numbers of imaginary quadratic fields

Journal Article (Journal Article)

For any odd prime l, let hl(-d)denote the l-part of the class number of the imaginary quadratic field Q(d). Nontrivial pointwise upper bounds are known only for ; nontrivial upper bounds for averages of have previously been known only for averages of hl(-d). In this paper we prove nontrivial upper bounds for the average of for all primesl≥7, as well as nontrivial upper bounds for certain higher moments for all primes ≥3.

Full Text

Duke Authors

Cited Authors

  • Heath-Brown, DR; Pierce, LB

Published Date

  • November 1, 2017

Published In

Volume / Issue

  • 153 / 11

Start / End Page

  • 2287 - 2309

International Standard Serial Number (ISSN)

  • 0010-437X

Digital Object Identifier (DOI)

  • 10.1112/S0010437X1700728X

Citation Source

  • Scopus