LEADER 04124nam 2200577 450 001 996466474003316 005 20220819112723.0 010 $a3-540-46659-2 024 7 $a10.1007/BFb0092305 035 $a(CKB)1000000000437103 035 $a(SSID)ssj0000326479 035 $a(PQKBManifestationID)12124663 035 $a(PQKBTitleCode)TC0000326479 035 $a(PQKBWorkID)10296580 035 $a(PQKB)10504600 035 $a(DE-He213)978-3-540-46659-8 035 $a(MiAaPQ)EBC5596483 035 $a(Au-PeEL)EBL5596483 035 $a(OCoLC)1076235436 035 $a(MiAaPQ)EBC6812383 035 $a(Au-PeEL)EBL6812383 035 $a(OCoLC)1287130174 035 $a(PPN)15520792X 035 $a(EXLCZ)991000000000437103 100 $a20220819d1992 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe Selberg-Arthur trace formula $ebased on lectures by James Arthur /$fSalahoddin Shokranian 205 $a1st ed. 1992. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d1992. 215 $a1 online resource (IX, 99 p.) 225 1 $aLecture Notes in Mathematics ;$vVolume 1503 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-55021-6 327 $aContents: Number Theory and Automorphic Representations: Some problems in classical number theory. Modular forms and automorphic representations -- Selberg's Trace Formula: Historical Remarks. Orbital integrals and Selberg's trace formula. Three examples. A necessary condition. Generalizations and applications -- Kernel Functions and the Convergence Theorem: Preliminaries on GL(r). Combinatorics and reduction theory. The convergence theorem -- The Adélic Theory: Basic facts -- The Geometric Theory: The JTO(f) and JT(f) distributions. A geometric I-function. The weight functions -- The Geometric Expansion of the Trace Formula: Weighted orbital integrals. The unipotent distribution -- The Spectral Theory: A review of the Eisenstein series. Cusp forms, truncation, the trace formula -- The Invariant Trace Formula and Its Applications: The in- variant trace formula for GL(r). Applications and remarks -- Bibliography -- Subject Index. 330 $aThis book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vVolume 1503. 606 $aSelberg trace formula 615 0$aSelberg trace formula. 676 $a512.7 700 $aShokranian$b Salahoddin$f1948-$059550 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466474003316 996 $aThe Selberg-Arthur Trace Formula$92860428 997 $aUNISA