Les Conjectures de Stark sur les Fonctions L d'Artin en s=0 - Notes d'un cours a Orsay redigees par Dominique Bernardi

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 12^th problem on the generalization of class fields by the values of transcendental functions.
This volume also treats these topics: a proof of the main conjecture for rational characters, and Chinburg's invariant; P. Delgne's proof of a function field analogue; p-adic versions of the conjectures due to B. Gross and J.-P. Serre.
This volume belongs on the shelf of every mathematics library.

List 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.

Product details

• Authors: J Tate, J. Tate
• Publisher: Springer, Basel
• Languages: French
• Product format: Hardback
• Released: 26.06.2009
• EAN: 9780817631888
• ISBN: 978-0-8176-3188-8
• No. of pages: 148
• Dimensions: 159 mm x 238 mm x 15 mm
• Weight: 399 g
• Illustrations: IV, 148 p.
• Series: Progress in Mathematics; Progress in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra