03306nam 2200637 450 99646665590331620230420151324.03-540-45178-110.1007/b13348(CKB)1000000000233140(SSID)ssj0000325192(PQKBManifestationID)11230897(PQKBTitleCode)TC0000325192(PQKBWorkID)10320768(PQKB)10141185(DE-He213)978-3-540-45178-5(MiAaPQ)EBC5591541(Au-PeEL)EBL5591541(OCoLC)1066195787(MiAaPQ)EBC6842517(Au-PeEL)EBL6842517(EXLCZ)99100000000023314020220912d2003 uy 0engurnn#008mamaatxtccrNon-Archimedean L-functions and arithmetical Siegel modular forms /Michel Courtieu, Alexei PanchishkinSecond edition.Berlin, Germany ;New York, New York :Springer-Verlag,[2003]©20031 online resource (VIII, 204 p.)Lecture Notes in Mathematics,0075-8434 ;1471Bibliographic Level Mode of Issuance: Monograph3-540-40729-4 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 super singular reduction of elliptic curves and abelian varieties). The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book could be very useful for postgraduate students and for non-experts giving a quick access to a rapidly developing domain of algebraic number theory: the arithmetical theory of L-functions and modular forms.Lecture Notes in Mathematics,0075-8434 ;1471L-functionsSiegel domainsModular groupsL-functions.Siegel domains.Modular groups.512.7311R54msc11F41mscCourtieu Michel1973-151489MiAaPQMiAaPQMiAaPQBOOK996466655903316Non-Archimedean L-functions and arithmetical Siegel modular forms271805UNISA