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＜電子ブック＞
Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms / by Michel Courtieu, Alexei A. Panchishkin
(Lecture Notes in Mathematics. ISSN:16179692 ; 1471)

版	2nd ed. 1991.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1991
大きさ	VIII, 204 p : online resource
著者標目	*Courtieu, Michel author Panchishkin, Alexei A author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Algebraic geometry FREE:Number Theory FREE:Algebraic Geometry
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/b13348

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