Error estimates for the davenport-heilbronn theorems

Karim Belabas, Manjul Bhargava, Carl Pomerance

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

We obtain the first known power-saving remainder terms for the theorems of Davenport and Heilbronn on the density of discriminants of cubic fields and the mean number of 3-torsion elements in the class groups of quadratic fields. In addition, we prove analogous error terms for the density of discriminants of quartic fields and the mean number of 2-torsion elements in the class groups of cubic fields. These results prove analytic continuation of the related Dirichlet series to the left of the line k(s) = 1.

Original languageEnglish (US)
Pages (from-to)173-210
Number of pages38
JournalDuke Mathematical Journal
Volume153
Issue number1
DOIs
StatePublished - May 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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