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© 1991

Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms

Second, Augmented Edition

  • Authors
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1471)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Michel Courtieu, Alexei A. Panchishkin
    Pages 1-12
  3. Michel Courtieu, Alexei A. Panchishkin
    Pages 13-44
  4. Michel Courtieu, Alexei A. Panchishkin
    Pages 45-93
  5. Michel Courtieu, Alexei A. Panchishkin
    Pages 95-125
  6. Michel Courtieu, Alexei A. Panchishkin
    Pages 187-193
  7. Back Matter
    Pages 195-196

About this book

Introduction

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.

Keywords

Eisenstein distributions distribution measures modular forms number theory

Bibliographic information

  • Book Title Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms
  • Book Subtitle Second, Augmented Edition
  • Authors Michel Courtieu
    Alexei A. Panchishkin
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title LNM
  • DOI https://doi.org/10.1007/b13348
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-40729-4
  • eBook ISBN 978-3-540-45178-5
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 2
  • Number of Pages VIII, 204
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published under: Panchishkin, A.A.
  • Topics Number Theory
    Algebraic Geometry
  • Buy this book on publisher's site
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Reviews

From the reviews of the second edition:

"The book is an updated version of the book ‘Non-Archimedean L-Functions of Hilbert and Siegel Modular Forms’ by Alexei Panchishkin published in 1991 … . The main subject of the book is the p-adic theory of L-functions of Siegel modular forms. … The basic new feature of this second version is the use of arithmetical nearly holomorphic Siegel modular forms … . The book will be very useful for postgraduate students and researchers entering this difficult area of research." (Andrzej Dabrowski, Zentralblatt MATH, Vol. 1070, 2005)