Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms
Authors: Courtieu, Michel, Panchishkin, Alexei A.
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- About this book
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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
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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)
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Introduction
Pages 1-12
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1 Non-Archimedean analytic functions, measures and distributions
Pages 13-44
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2 Siegel modular forms and the holomorphic projection operator
Pages 45-93
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3 Arithmetical differential operators on nearly holomorphic Siegel modular forms
Pages 95-125
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4 Admissible measures for standard L–functions and nearly holomorphic Siegel modular forms
Pages 127-186
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms
- Authors
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- Michel Courtieu
- Alexei A. Panchishkin
- 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
