Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms /
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...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
1991.
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| Series: | Lecture Notes in Mathematics, Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn - vol. 16 ;
1471. |
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| Online Access: | Connect to the full text of this electronic book |
| 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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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (VII, 161 pages) : online resource. |
| ISBN: | 9783662215418 (electronic bk.) 3662215411 (electronic bk.) |