Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms / by Alexey A. Panchishkin.

Format:

Book

Author/Creator:

Panchishkin, Alexey A., author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1471.

Lecture Notes in Mathematics, 0075-8434 ; 1471

Language:

English

Subjects (All):

Number theory.

Geometry, Algebraic.

Number Theory.

Algebraic Geometry.

Local Subjects:

Number Theory.

Algebraic Geometry.

Physical Description:

1 online resource (VII, 161 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991.

System Details:

text file PDF

Summary:

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 supersingular reduction of ellptic curves and abelian varieties). The given construction of these p-adic L-functions uses precise algebraic properties of the arihmetical Shimura differential operator. The book could be very useful for postgraduate students and for non-experts giving a quick access to a rapidly developping domain of algebraic number theory: the arithmetical theory of L-functions and modular forms.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783662215418

Access Restriction:

Restricted for use by site license.