Non-archimedean L-functions and arithmetical Siegel modular forms

Michel Courtieu, Alexei Panchishkin - Collection Lectures Notes in Mathematics

204 pages, parution le 17/12/2003 (2^eme édition)

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Résumé

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.

Non-Archimedean analytic functions, measures and distributions
Siegel modular forms and the holomorphic projection operator
Arithmetical differential operators
Admissible measures for standard L-functions
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Michel Courtieu, Alexei Panchishkin
Collection	Lectures Notes in Mathematics
Parution	17/12/2003
Édition	2^eme édition
Nb. de pages	204
Format	15,5 x 23,5
Couverture	Broché
Poids	320g
Intérieur	Noir et Blanc
EAN13	9783540407294