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Upper Bounds on |L(1, χ)| and Applications

Published online by Cambridge University Press:  20 November 2018

Stéphane Louboutin
Stéphane Louboutin*
Affiliation:
Université de Caen, UFR Sciences, Département de Mathématiques, 14032 Caen cedex, France
*
e-mail: loubouti@math.unicaen.fr
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Abstract

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We give upper bounds on the modulus of the values at $s\,=\,1$ of Artin $L$-functions of abelian extensions unramified at all the infinite places. We also explain how we can compute better upper bounds and explain how useful such computed bounds are when dealing with class number problems for $\text{CM}$-fields. For example, we will reduce the determination of all the non-abelian normal $\text{CM}$-fields of degree 24 with Galois group $\text{S}{{\text{L}}_{\text{2}}}\left( {{F}_{3}} \right)$ (the special linear group over the finite field with three elements) which have class number one to the computation of the class numbers of 23 such $\text{CM}$-fields.

Keywords

11M2011R4211Y3511R29Dedekind zeta functionDirichlet seriesCM-fieldrelative class number
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 4 , 01 August 1998 , pp. 794 - 815
Copyright
Copyright © Canadian Mathematical Society 1998

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