Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms: 1471 - Brossura

Courtieu, Michel

Brossura

ISBN 10: 3540407294 ISBN 13: 9783540407294

Casa editrice: Springer, 2009

Riassunto

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.

Su questo libro

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 3540407294
• ISBN 13: 9783540407294
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 212
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania