03362nam 2200637 450 99646659550331620220704070743.03-662-21541-110.1007/978-3-662-21541-8(CKB)3390000000043617(SSID)ssj0001091439(PQKBManifestationID)11993011(PQKBTitleCode)TC0001091439(PQKBWorkID)11027506(PQKB)11431471(DE-He213)978-3-662-21541-8(MiAaPQ)EBC5592495(Au-PeEL)EBL5592495(OCoLC)1066196485(MiAaPQ)EBC6842855(Au-PeEL)EBL6842855(OCoLC)1292363437(PPN)238023710(EXLCZ)99339000000004361720220306d1991 uy 0engurnn#008mamaatxtccrNon-archimedean L-functions of Siegel and Hilbert modular forms /Alexey A. Panchishkin1st ed. 1991.Berlin ;Heidelberg :Springer-Verlag GmbH,1991.1 online resource (VII, 161 p.)Lecture notes in mathematics ;1471Bibliographic Level Mode of Issuance: Monograph3-540-54137-3 Includes bibliographical references and index.Content -- Acknowledgement -- 1. Non-Archimedean analytic functions, measures and distributions -- 2. Siegel modular forms and the holomorphic projection operator -- 3. Non-Archimedean standard zeta functions of Siegel modular forms -- 4. Non-Archimedean convolutions of Hilbert modular forms -- References.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 (Springer-Verlag) ;1471.L-functionsSiegel domainsHilbert modular surfacesL-functions.Siegel domains.Hilbert modular surfaces.512.73Pančiškin A. A(Aleksej Alekseevič),1221095MiAaPQMiAaPQMiAaPQBOOK996466595503316Non-archimedean L-functions of Siegel and Hilbert modular forms2831160UNISA