Non-Archimedean L-Functions [electronic resource] of Siegel and Hilbert Modular Forms / by Alexei A. Panchishkin.
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...
Uniform Title: | Lecture Notes in Mathematics,
1617-9692 ; 1471 |
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Main Author: | |
Corporate Author: | |
Language: | English |
Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
1991.
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Edition: | 1st ed. 1991. |
Series: | Lecture Notes in Mathematics,
1471 |
Subjects: | |
Online Access: | |
Variant Title: |
Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms |
Format: | Electronic eBook |
Summary: |
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. |
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ISBN: | 9783662215418 (online) |
ISSN: | 1617-9692 ; |