UID:
almafu_9959186583302883
Format:
1 online resource (VIII, 204 p.)
Edition:
2nd ed. 1991.
Edition:
Online edition Berlin [u.a.] Springer Springer Lecture Notes Archive ; 041142-5
ISBN:
3-540-45178-1
Series Statement:
Lecture Notes in Mathematics, 1471
Content:
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.
Note:
Bibliographic Level Mode of Issuance: Monograph
,
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.
,
English
Additional Edition:
ISBN 3-540-40729-4
Language:
English
Subjects:
Mathematics
Keywords:
Online-Publikation
URL:
http://dx.doi.org/10.1007/b13348
