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Explicit Upper Bounds for Residues of Dedekind Zeta Functions and Values of L-Functions at s = 1, and Explicit Lower Bounds for Relative Class Numbers of CM-Fields

Published online by Cambridge University Press:  20 November 2018

Stéphane Louboutin
Stéphane Louboutin*
Affiliation:
Institut de Mathématiques de Luminy, UPR 906, 163, avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France. email: loubouti@iml.univ-mrs.fr
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Abstract

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We provide the reader with a uniform approach for obtaining various useful explicit upper bounds on residues of Dedekind zeta functions of numbers fields and on absolute values of values at $s=1$ of $L$-series associated with primitive characters on ray class groups of number fields. To make it quite clear to the reader how useful such bounds are when dealing with class number problems for CM-fields, we deduce an upper bound for the root discriminants of the normal CM-fields with (relative) class number one.

Keywords

11R4211R29Dedekind zeta functionsL-functionsrelative class numbersCM-fields
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 6 , 01 December 2001 , pp. 1194 - 1222
Copyright
Copyright © Canadian Mathematical Society 2001

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