1.

Record Nr.

UNISA996466655903316

Autore

Courtieu Michel <1973->

Titolo

Non-Archimedean L-functions and arithmetical Siegel modular forms / / Michel Courtieu, Alexei Panchishkin

Pubbl/distr/stampa

Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [2003]

©2003

ISBN

3-540-45178-1

Edizione

[Second edition.]

Descrizione fisica

1 online resource (VIII, 204 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1471

Classificazione

11R54

11F41

Disciplina

512.73

Soggetti

L-functions

Siegel domains

Modular groups

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di contenuto

Introduction -- Non-Archimedean analytic functions, measures and distributions -- Siegel modular forms and the holomorphic projection operator -- Arithmetical differential operators on nearly holomorphic Siegel modular forms -- Admissible measures for standard L-functions and nearly holomorphic Siegel modular forms.

Sommario/riassunto

This book 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 (which were first introduced by Amice, Velu and Vishik in the elliptic modular case when they come from a good super singular reduction of elliptic curves and abelian varieties). The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book could be very useful for postgraduate students and for non-experts giving a quick access to a



rapidly developing domain of algebraic number theory: the arithmetical theory of L-functions and modular forms.