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15 May 2010 Error estimates for the Davenport-Heilbronn theorems
Karim Belabas, Manjul Bhargava, Carl Pomerance
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Duke Math. J. 153(1): 173-210 (15 May 2010). DOI: 10.1215/00127094-2010-007

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 R(s)=1.

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Karim Belabas. Manjul Bhargava. Carl Pomerance. "Error estimates for the Davenport-Heilbronn theorems." Duke Math. J. 153 (1) 173 - 210, 15 May 2010. https://doi.org/10.1215/00127094-2010-007

Information

Published: 15 May 2010
First available in Project Euclid: 28 April 2010

zbMATH: 1227.11114
MathSciNet: MR2641942
Digital Object Identifier: 10.1215/00127094-2010-007

Subjects:
Primary: 11R11
Secondary: 11R29, 11R45

Rights: Copyright © 2010 Duke University Press

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Vol.153 • No. 1 • 15 May 2010
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