Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms

  • Alexey A. Panchishkin

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

Table of contents

  1. Front Matter
    Pages N2-vii
  2. Alexey A. Panchishkin
    Pages 1-8
  3. Alexey A. Panchishkin
    Pages 8-8
  4. Alexey A. Panchishkin
    Pages 117-145
  5. Back Matter
    Pages 146-161

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.


11F 11R 11S 19K 46F 46G Eisenstein distributions measures modular forms analytic function convolution distribution zeta function

Authors and affiliations

  • Alexey A. Panchishkin
    • 1
  1. 1.Department of MathematicsMoscow State UniversityMoscowUSSR

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54137-0
  • Online ISBN 978-3-662-21541-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site