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Lecture Notes in Mathematics

Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms

Authors: Courtieu, Michel, Panchishkin, Alexei A.

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eBook 29,74 €
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  • ISBN 978-3-540-45178-5
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  • Immediate eBook download after purchase
Softcover 36,35 €
price for Spain (gross)
  • ISBN 978-3-540-40729-4
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  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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

    Preview Buy Chapter 30,19 €
  • 1 Non-Archimedean analytic functions, measures and distributions

    Courtieu, Michel (et al.)

    Pages 13-44

    Preview Buy Chapter 30,19 €
  • 2 Siegel modular forms and the holomorphic projection operator

    Courtieu, Michel (et al.)

    Pages 45-93

    Preview Buy Chapter 30,19 €
  • 3 Arithmetical differential operators on nearly holomorphic Siegel modular forms

    Courtieu, Michel (et al.)

    Pages 95-125

    Preview Buy Chapter 30,19 €
  • 4 Admissible measures for standard L–functions and nearly holomorphic Siegel modular forms

    Courtieu, Michel (et al.)

    Pages 127-186

    Preview Buy Chapter 30,19 €

Buy this book

eBook 29,74 €
price for Spain (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 36,35 €
price for Spain (gross)
  • ISBN 978-3-540-40729-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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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