Les conjectures de Stark sur les fonctions L d'Artin en s=O : notes d'un cours à Orsay

Bibliographic Information

Les conjectures de Stark sur les fonctions L d'Artin en s=O : notes d'un cours à Orsay

John Tate ; rédigées par Dominique Bernardi et Norbert Schappacher

(Progress in mathematics, v. 47)

Birkhäuser, 1984

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Note

Bibliography: p. 139-143

Description and Table of Contents

Description

This book presents a self-contained introduction to H.M. Stark's remarkable conjectures about the leading term of the Taylor expansion of Artin's L-functions at s=0. These conjectures can be viewed as a vast generalization of Dirichlet's class number formula and Kronecker's limit formula. They provide an unexpected contribution to Hilbert's 12th problem on the generalization of class fields by the values of transcendental functions. This volume belongs on the shelf of every mathematics library.

Table of Contents

Introduction.-Fonctions L D'Artin.-La Conjecture Principale de Stark.-Caracteres a Valeurs Rationnelles.-Les Cas r(x)=0 et r(x)=1.-La Conjecture Plus Fine Dans le Cas Abelien.-Le Cas Des Corps de Fonctions.-Analogues p-Adiques des Conjectures de Stark.-Bibliographie.

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