Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms

2. Auflage 1991
ISBN: 978-3-540-40729-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1471, 204 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 330 g

Reihe: Lecture Notes in Mathematics

This book, now in its 2nd edition, 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. The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator.

The book will be very useful for postgraduate students and for non-experts looking for a quick approach to a rapidly developing domain of algebraic number theory. This new edition is substantially revised to account for the new explanations that have emerged in the past 10 years of the main formulas for special L-values in terms of arithmetical theory of nearly holomorphic modular forms.

Zielgruppe

Research

Autoren/Hrsg.

Panchishkin, Alexei A.

Courtieu, Michel

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

Introduction.- Non-Archimedean analytic functions, measures and distributions.- Siegel modular forms and the holomorphic projection operator.- Arithmetical differential operators on nearly holomorphic Siegel modular forms.- Admissible measures for standard L-functions and nearly holomorphic Siegel modular forms.