LEADER 03333nam 2200637 450 001 996466498003316 005 20220305130631.0 010 $a3-540-39331-5 024 7 $a10.1007/BFb0077696 035 $a(CKB)1000000000437552 035 $a(SSID)ssj0000321367 035 $a(PQKBManifestationID)12133177 035 $a(PQKBTitleCode)TC0000321367 035 $a(PQKBWorkID)10279529 035 $a(PQKB)11563547 035 $a(DE-He213)978-3-540-39331-3 035 $a(MiAaPQ)EBC5586187 035 $a(Au-PeEL)EBL5586187 035 $a(OCoLC)1066188358 035 $a(MiAaPQ)EBC6842840 035 $a(Au-PeEL)EBL6842840 035 $a(OCoLC)1159635985 035 $a(PPN)155215493 035 $a(EXLCZ)991000000000437552 100 $a20220305d1987 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 13$aAn approach to the Selberg trace formula via the Selberg zeta-function /$fJurgen Fischer 205 $a1st ed. 1987. 210 1$aBerlin :$cSpringer-Verlag,$d1987. 215 $a1 online resource (IV, 188 p.) 225 1 $aLecture notes in mathematics (Springer-Verlag) ;$v1253 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-15208-3 320 $aIncludes bibliographical references and indexes. 327 $aBasic facts -- The trace of the iterated resolvent kernel -- The entire function ? associated with the selberg zeta-function -- The general selberg trace formula. 330 $aThe Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the Selberg zeta-function. Previous knowledge of the Selberg trace formula is not assumed. The theory is developed for arbitrary real weights and for arbitrary multiplier systems permitting an approach to known results on classical automorphic forms without the Riemann-Roch theorem. The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function. For example, the canonical factorization theorem involves an analogue of the Euler constant. Finally the general Selberg trace formula is deduced easily from the properties of the Selberg zeta-function: this is similar to the procedure in analytic number theory where the explicit formulae are deduced from the properties of the Riemann zeta-function. Apart from the basic spectral theory of the Laplacian for cofinite groups the book is self-contained and will be useful as a quick approach to the Selberg zeta-function and the Selberg trace formula. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1253. 606 $aFunctions, Zeta 606 $aNumber theory 606 $aSelberg trace formula 615 0$aFunctions, Zeta. 615 0$aNumber theory. 615 0$aSelberg trace formula. 676 $a515.56 700 $aFischer$b Ju?rgen$056736 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466498003316 996 $aApproach to the Selberg trace formula via the Selberg zeta-function$978544 997 $aUNISA