LEADER 03306nam 2200637 450 001 996466655903316 005 20230420151324.0 010 $a3-540-45178-1 024 7 $a10.1007/b13348 035 $a(CKB)1000000000233140 035 $a(SSID)ssj0000325192 035 $a(PQKBManifestationID)11230897 035 $a(PQKBTitleCode)TC0000325192 035 $a(PQKBWorkID)10320768 035 $a(PQKB)10141185 035 $a(DE-He213)978-3-540-45178-5 035 $a(MiAaPQ)EBC5591541 035 $a(Au-PeEL)EBL5591541 035 $a(OCoLC)1066195787 035 $a(MiAaPQ)EBC6842517 035 $a(Au-PeEL)EBL6842517 035 $a(EXLCZ)991000000000233140 100 $a20220912d2003 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNon-Archimedean L-functions and arithmetical Siegel modular forms /$fMichel Courtieu, Alexei Panchishkin 205 $aSecond edition. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[2003] 210 4$dİ2003 215 $a1 online resource (VIII, 204 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1471 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-40729-4 327 $aIntroduction -- 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. 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,$x0075-8434 ;$v1471 606 $aL-functions 606 $aSiegel domains 606 $aModular groups 615 0$aL-functions. 615 0$aSiegel domains. 615 0$aModular groups. 676 $a512.73 686 $a11R54$2msc 686 $a11F41$2msc 700 $aCourtieu$b Michel$f1973-$0151489 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466655903316 996 $aNon-Archimedean L-functions and arithmetical Siegel modular forms$9271805 997 $aUNISA