This book presents a self-contained introduction to H.M. Starkâs remarkable conjectures about the leading term of the Taylor expansion of Artinâs L-functions at s=0. These conjectures can be viewed as a vast generalization of Dirichletâs class number formula and Kroneckerâs limit formula. They provide an unexpected contribution to Hilbertâs 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 Chinburgâs invariant; P. Delgneâs 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.
