LEADER 03362nam 2200637 450 001 996466595503316 005 20220704070743.0 010 $a3-662-21541-1 024 7 $a10.1007/978-3-662-21541-8 035 $a(CKB)3390000000043617 035 $a(SSID)ssj0001091439 035 $a(PQKBManifestationID)11993011 035 $a(PQKBTitleCode)TC0001091439 035 $a(PQKBWorkID)11027506 035 $a(PQKB)11431471 035 $a(DE-He213)978-3-662-21541-8 035 $a(MiAaPQ)EBC5592495 035 $a(Au-PeEL)EBL5592495 035 $a(OCoLC)1066196485 035 $a(MiAaPQ)EBC6842855 035 $a(Au-PeEL)EBL6842855 035 $a(OCoLC)1292363437 035 $a(PPN)238023710 035 $a(EXLCZ)993390000000043617 100 $a20220306d1991 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNon-archimedean L-functions of Siegel and Hilbert modular forms /$fAlexey A. Panchishkin 205 $a1st ed. 1991. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag GmbH,$d1991. 215 $a1 online resource (VII, 161 p.) 225 1 $aLecture notes in mathematics ;$v1471 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-54137-3 320 $aIncludes bibliographical references and index. 327 $aContent -- 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. 330 $aThis book is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth (which were first introduced by Amice, Velu and Vishik in the elliptic modular case when they come from a good super singular reduction of elliptic curves and abelian varieties). The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book could be very useful for postgraduate students and for non-experts giving a quick access to a rapidly developing domain of algebraic number theory: the arithmetical theory of L-functions and modular forms. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1471. 606 $aL-functions 606 $aSiegel domains 606 $aHilbert modular surfaces 615 0$aL-functions. 615 0$aSiegel domains. 615 0$aHilbert modular surfaces. 676 $a512.73 700 $aPanc?is?kin$b A. A$g(Aleksej Alekseevic?),$01221095 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466595503316 996 $aNon-archimedean L-functions of Siegel and Hilbert modular forms$92831160 997 $aUNISA