Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms

Author:   Michel Courtieu ,  Alexei A. Panchishkin
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition:   2nd ed. 1991
Volume:   1471
ISBN:  

9783540407294


Pages:   204
Publication Date:   05 December 2003
Format:   Paperback
Availability:   In Print   Availability explained
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Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms


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Overview

This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are 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-functions treated 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-experts looking for a 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.

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