This book presents a self-contained introduction to H.M. Starka (TM)s remarkable conjectures about the leading term of the Taylor expansion of Artina (TM)s L-functions at s=0. These conjectures can be viewed as a vast generalization of Dirichleta (TM)s class number formula and Kroneckera (TM)s limit formula. They provide an unexpected contribution to Hilberta (TM)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 Chinburga (TM)s invariant; P. Delgnea (TM)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. Less
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