Lecture Notes in Mathematics

Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms

Authors: Courtieu, Michel, Panchishkin, Alexei A.

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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.

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)


Table of contents (6 chapters)

  • Introduction

    Courtieu, Michel (et al.)

    Pages 1-12

  • 1 Non-Archimedean analytic functions, measures and distributions

    Courtieu, Michel (et al.)

    Pages 13-44

  • 2 Siegel modular forms and the holomorphic projection operator

    Courtieu, Michel (et al.)

    Pages 45-93

  • 3 Arithmetical differential operators on nearly holomorphic Siegel modular forms

    Courtieu, Michel (et al.)

    Pages 95-125

  • 4 Admissible measures for standard L–functions and nearly holomorphic Siegel modular forms

    Courtieu, Michel (et al.)

    Pages 127-186

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-540-45178-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-40729-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1471
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-45178-5
DOI
10.1007/b13348
Softcover ISBN
978-3-540-40729-4
Series ISSN
0075-8434
Edition Number
2
Number of Pages
VIII, 204
Additional Information
Originally published under: Panchishkin, A.A.
Topics