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