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

Notes d'un cours a Orsay redigees par Dominique Bernardi
1984
ISBN: 978-0-8176-3188-8
Verlag: Birkhäuser Boston

Buch, Französisch, Band 47, 148 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 407 g

Reihe: Progress in Mathematics

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 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.

Zielgruppe

Research

Autoren/Hrsg.

Tate, J.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.