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Averages and moments associated to class numbers of imaginary quadratic fields.
- Source :
-
Compositio Mathematica . Nov2017, Vol. 153 Issue 11, p2287-2309. 23p. - Publication Year :
- 2017
-
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 $\ell \geqslant 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\ell \geqslant 3$. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 0010437X
- Volume :
- 153
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Compositio Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 124617057
- Full Text :
- https://doi.org/10.1112/S0010437X1700728X