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NON-ARCHIMEDEAN L-FUNCTIONS AND ARITHMETICAL SIEGEL MODULAR IBD

ALEXEI A PANCHISHKIN / MICHEL COURTIEU
SPRINGER
12 / 2003
9783540407294
Inglés

Sinopsis

This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central objectáare L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functionsátreated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth. The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book will be very useful for postgraduate students and for non-expertsálooking foráa quick approach to a rapidly developing domain of algebraic number theory. This new edition is substantially revised to account for the new explanations that have emerged in the past 10 years of the main formulas for special L-values in terms of arithmetical theory of nearly holomorphic modular forms.

PVP
60,47€