LEADER 07099nam 22018015 450 001 9910154753203321 005 20190708092533.0 010 $a1-4008-8161-7 024 7 $a10.1515/9781400881611 035 $a(CKB)3710000000620135 035 $a(SSID)ssj0001651234 035 $a(PQKBManifestationID)16426389 035 $a(PQKBTitleCode)TC0001651234 035 $a(PQKBWorkID)14719076 035 $a(PQKB)11404407 035 $a(MiAaPQ)EBC4738541 035 $a(DE-B1597)467924 035 $a(OCoLC)979968791 035 $a(DE-B1597)9781400881611 035 $a(EXLCZ)993710000000620135 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAutomorphic Forms on Adele Groups. (AM-83), Volume 83 /$fStephen S. Gelbart 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$d©1975 215 $a1 online resource (280 pages) 225 0 $aAnnals of Mathematics Studies ;$v262 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-691-08156-5 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tPREFACE -- $tCONTENTS -- $t§1. THE CLASSICAL THEORY -- $t§2. AUTOMORPHIC FORMS AND THE DECOMPOSITION OF L2(?SL(2,?)) -- $t§3. AUTOMORPHIC FORMS AS FUNCTIONS ON THE ADELE GROUP OF GL(2) -- $t§4. THE REPRESENTATIONS OF GL(2) OVER LOCAL AND GLOBAL FIELDS -- $t§5 . CUSP FORMS AND REPRESENTATIONS OF THE ADELE GROUP OF GL(2) -- $t§6. HECKE THEORY FOR GL(2) -- $t§7 . THE CONSTRUCTION OF A SPECIAL CLASS OF AUTOMORPHIC FORMS -- $t§ 8 . EISENSTEIN SERIES AND THE CONTINUOUS SPECTRUM -- $t§9. THE TRACE FORMULA FOR GL(2) -- $t§10. AUTOMORPHIC FORMS ON A QUATERNION ALGEBRA -- $tBIBLIOGRAPHY -- $tINDEX 330 $aThis volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory.TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr? 410 0$aAnnals of mathematics studies ;$vNumber 83. 606 $aRepresentations of groups 606 $aAutomorphic forms 606 $aLinear algebraic groups 606 $aAdeles 610 $aAbelian extension. 610 $aAbelian group. 610 $aAbsolute value. 610 $aAddition. 610 $aAdditive group. 610 $aAlgebraic group. 610 $aAlgebraic number field. 610 $aAlgebraic number theory. 610 $aAnalytic continuation. 610 $aAnalytic function. 610 $aArbitrarily large. 610 $aAutomorphic form. 610 $aCartan subgroup. 610 $aClass field theory. 610 $aComplex space. 610 $aCongruence subgroup. 610 $aConjugacy class. 610 $aCoprime integers. 610 $aCusp form. 610 $aDifferential equation. 610 $aDimension (vector space). 610 $aDirect integral. 610 $aDirect sum. 610 $aDivision algebra. 610 $aEigenfunction. 610 $aEigenvalues and eigenvectors. 610 $aEisenstein series. 610 $aEuler product. 610 $aExistential quantification. 610 $aExponential function. 610 $aFactorization. 610 $aFinite field. 610 $aFormal power series. 610 $aFourier series. 610 $aFourier transform. 610 $aFuchsian group. 610 $aFunction (mathematics). 610 $aFunction space. 610 $aFunctional equation. 610 $aFundamental unit (number theory). 610 $aGalois extension. 610 $aGlobal field. 610 $aGroup algebra. 610 $aGroup representation. 610 $aHaar measure. 610 $aHarish-Chandra. 610 $aHecke L-function. 610 $aHilbert space. 610 $aHomomorphism. 610 $aInduced representation. 610 $aInfinite product. 610 $aInner automorphism. 610 $aInteger. 610 $aInvariant measure. 610 $aInvariant subspace. 610 $aIrreducible representation. 610 $aL-function. 610 $aLie algebra. 610 $aLinear map. 610 $aMatrix coefficient. 610 $aMellin transform. 610 $aMeromorphic function. 610 $aModular form. 610 $aP-adic number. 610 $aPoisson summation formula. 610 $aPrime ideal. 610 $aPrime number. 610 $aPrincipal series representation. 610 $aProjective representation. 610 $aQuadratic field. 610 $aQuadratic form. 610 $aQuaternion algebra. 610 $aQuaternion. 610 $aReal number. 610 $aRegular representation. 610 $aRepresentation theory. 610 $aRing (mathematics). 610 $aRing of integers. 610 $aScientific notation. 610 $aSelberg trace formula. 610 $aSimple algebra. 610 $aSquare-integrable function. 610 $aSub"ient. 610 $aSubgroup. 610 $aSummation. 610 $aTheorem. 610 $aTheory. 610 $aTheta function. 610 $aTopological group. 610 $aTopology. 610 $aTrace formula. 610 $aTrivial representation. 610 $aUniqueness theorem. 610 $aUnitary operator. 610 $aUnitary representation. 610 $aUniversal enveloping algebra. 610 $aUpper half-plane. 610 $aVariable (mathematics). 610 $aVector space. 610 $aWeil group. 615 0$aRepresentations of groups. 615 0$aAutomorphic forms. 615 0$aLinear algebraic groups. 615 0$aAdeles. 676 $a512/.22 700 $aGelbart$b Stephen S., $045743 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154753203321 996 $aAutomorphic Forms on Adele Groups. (AM-83), Volume 83$92788530 997 $aUNINA LEADER 03357nam 22007815 450 001 9910483471303321 005 20251225173540.0 010 $a3-030-73128-6 024 7 $a10.1007/978-3-030-73128-1 035 $a(CKB)4100000011867287 035 $a(MiAaPQ)EBC6533364 035 $a(Au-PeEL)EBL6533364 035 $a(OCoLC)1245674918 035 $a(PPN)255289383 035 $a(BIP)79756724 035 $a(BIP)79363328 035 $a(DE-He213)978-3-030-73128-1 035 $a(EXLCZ)994100000011867287 100 $a20210401d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRequirements Engineering: Foundation for Software Quality $e27th International Working Conference, REFSQ 2021, Essen, Germany, April 12?15, 2021, Proceedings /$fedited by Fabiano Dalpiaz, Paola Spoletini 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (241 pages) $cillustrations 225 1 $aProgramming and Software Engineering,$x2945-9168 ;$v12685 311 08$a3-030-73127-8 320 $aIncludes bibliographical references and index. 327 $aNatural Language Processing and Machine Learning -- RE for AI-Enabled Systems -- From Software to Systems and Services -- Analysts' Competence and Training. 330 $aThis book constitutes the proceedings of the 27th International Working Conference on Requirements Engineering - Foundation for Software Quality, REFSQ 2021, which was due to be held in Essen, Germany, in April 2021. Due to the COVID-19 pandemic the conference was held virtually in April 2021. The special focus of this year`s REFSQ 2021 conference are contributions emphasizing the importance of human values, such as privacy and fairness, when designing software-intensive systems as well as the challenges that intelligent and autonomous systems pose due to the tight interplay with humans. 410 0$aProgramming and Software Engineering,$x2945-9168 ;$v12685 606 $aSoftware engineering 606 $aArtificial intelligence 606 $aInformation storage and retrieval systems 606 $aData mining 606 $aComputer networks 606 $aComputers 606 $aSoftware Engineering 606 $aArtificial Intelligence 606 $aInformation Storage and Retrieval 606 $aData Mining and Knowledge Discovery 606 $aComputer Communication Networks 606 $aComputing Milieux 615 0$aSoftware engineering. 615 0$aArtificial intelligence. 615 0$aInformation storage and retrieval systems. 615 0$aData mining. 615 0$aComputer networks. 615 0$aComputers. 615 14$aSoftware Engineering. 615 24$aArtificial Intelligence. 615 24$aInformation Storage and Retrieval. 615 24$aData Mining and Knowledge Discovery. 615 24$aComputer Communication Networks. 615 24$aComputing Milieux. 676 $a005.1 702 $aDalpiaz$b Fabiano 702 $aSpoletini$b Paola 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483471303321 996 $aRequirements Engineering$92143744 997 $aUNINA