Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms / Lecture Notes in Mathematics Bd.1471 (PDF)
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...
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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.
- Autoren: Michel Courtieu , Alexei A. Panchishkin
- 2003, 2nd ed. 1991, 204 Seiten, Englisch
- Verlag: Springer Berlin Heidelberg
- ISBN-10: 3540451781
- ISBN-13: 9783540451785
- Erscheinungsdatum: 09.12.2003
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- Grösse: 2.52 MB
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