J. Tate

Les Conjectures de Stark sur les Fonctions L d'Artin en s=0

Notes d'un cours a Orsay redigees par Dominique Bernardi

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Progress in Mathematics 47
• Verlag: Birkhäuser / Birkhäuser Boston / Springer, Basel
• Artikelnr. des Verlages: 978-0-8176-3188-8
• 1984.
• Seitenzahl: 156
• Erscheinungstermin: 1. Januar 1984
• Französisch
• Abmessung: 241mm x 160mm x 14mm
• Gewicht: 399g
• ISBN-13: 9780817631888
• ISBN-10: 0817631887
• Artikelnr.: 21686550

Inhaltsangabe

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.