Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms

Second, Augmented Edition

  • Authors
  • Michel Courtieu
  • Alexei A. Panchishkin

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


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.


Eisenstein distributions distribution measures modular forms number theory

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-40729-4
  • Online ISBN 978-3-540-45178-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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