1.

Record Nr.

UNISA996466595503316

Autore

Pančiškin A. A (Aleksej Alekseevič)

Titolo

Non-archimedean L-functions of Siegel and Hilbert modular forms / / Alexey A. Panchishkin

Pubbl/distr/stampa

Berlin ; ; Heidelberg : , : Springer-Verlag GmbH, , 1991

ISBN

3-662-21541-1

Edizione

[1st ed. 1991.]

Descrizione fisica

1 online resource (VII, 161 p.)

Collana

Lecture notes in mathematics ; ; 1471

Disciplina

512.73

Soggetti

L-functions

Siegel domains

Hilbert modular surfaces

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Content -- Acknowledgement -- 1. Non-Archimedean analytic functions, measures and distributions -- 2. Siegel modular forms and the holomorphic projection operator -- 3. Non-Archimedean standard zeta functions of Siegel modular forms -- 4. Non-Archimedean convolutions of Hilbert modular forms -- References.

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.