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

This book presents a self-contained introduction to H.M. Starks remarkable conjectures about the leading term of the Taylor expansion of Artins L-functions at s=0. These conjectures can be viewed as a vast generalization of Dirichlets class number formula and Kroneckers limit formula. They provide an unexpected contribution to Hilberts 12th 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 Chinburgs invariant; P. Delgnes 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.