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Leading terms of Artin L-functions at s=0 and s=1

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  01 November 2007

Manuel Breuning  and
David Burns
Manuel Breuning
Affiliation:
Department of Mathematics, King’s College London, Strand, London WC2R 2LS, UK (email: manuel.breuning@kcl.ac.uk, david.burns@kcl.ac.uk)
David Burns
Affiliation:
Department of Mathematics, King’s College London, Strand, London WC2R 2LS, UK (email: manuel.breuning@kcl.ac.uk, david.burns@kcl.ac.uk)
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Abstract

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We formulate an explicit conjecture for the leading term at s=1 of the equivariant Dedekind zeta-function that is associated to a Galois extension of number fields. We show that this conjecture refines well-known conjectures of Stark and Chinburg, and we use the functional equation of the zeta-function to compare it to a natural conjecture for the leading term at s=0.

Keywords

Artin L-functionsequivariant zeta-functionsleading termsfunctional equation

MSC classification

Secondary: 11R42: Zeta functions and $L$-functions of number fields 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers 11R34: Galois cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 6 , November 2007 , pp. 1427 - 1464
Copyright
Copyright © Foundation Compositio Mathematica 2007