About this book
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.
- Book Title Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms
- Series Title Lecture Notes in Mathematics
- DOI https://doi.org/10.1007/978-3-662-21541-8
- Copyright Information Springer-Verlag Berlin Heidelberg 1991
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Softcover ISBN 978-3-540-54137-0
- eBook ISBN 978-3-662-21541-8
- Series ISSN 0075-8434
- Series E-ISSN 1617-9692
- Edition Number 1
- Number of Pages VII, 161
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
- Additional Information Originally published under: Panchishkin, A.A.
- Buy this book on publisher's site
From the reviews of the second edition:
"The book is an updated version of the book ‘Non-Archimedean L-Functions of Hilbert and Siegel Modular Forms’ by Alexei Panchishkin published in 1991 … . The main subject of the book is the p-adic theory of L-functions of Siegel modular forms. … The basic new feature of this second version is the use of arithmetical nearly holomorphic Siegel modular forms … . The book will be very useful for postgraduate students and researchers entering this difficult area of research." (Andrzej Dabrowski, Zentralblatt MATH, Vol. 1070, 2005)