LEADER 03194nam 2200601 450 001 996466383803316 005 20220303131219.0 010 $a3-540-47762-4 024 7 $a10.1007/BFb0077660 035 $a(CKB)1000000000437561 035 $a(SSID)ssj0000324620 035 $a(PQKBManifestationID)12097576 035 $a(PQKBTitleCode)TC0000324620 035 $a(PQKBWorkID)10332235 035 $a(PQKB)10288858 035 $a(DE-He213)978-3-540-47762-4 035 $a(MiAaPQ)EBC5591058 035 $a(Au-PeEL)EBL5591058 035 $a(OCoLC)1066191574 035 $a(MiAaPQ)EBC6842790 035 $a(Au-PeEL)EBL6842790 035 $a(OCoLC)793078998 035 $a(PPN)155211110 035 $a(EXLCZ)991000000000437561 100 $a20220303d1987 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aManifolds with cusps of rank one $espectral theory and L2-index theorem /$fWerner Mu?ller 205 $a1st ed. 1987. 210 1$aBerlin :$cSpringer-Verlag,$d[1987] 210 4$dİ1987 215 $a1 online resource (X, 158 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1244 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-17696-9 311 $a3-540-17696-9 327 $aPreliminaries -- Cusps of rank one -- The heat equation on the cusp -- The Neumann laplacian on the cusp -- Manifolds with cusps of rank one -- The spectral resolution of H -- The heat kernel -- The eisenstein functions -- The spectral shift function -- The L2-index of generalized dirac operators -- The unipotent contribution to the index -- The Hirzebruch conjecture. 330 $aThe manifolds investigated in this monograph are generalizations of (XX)-rank one locally symmetric spaces. In the first part of the book the author develops spectral theory for the differential Laplacian operator associated to the so-called generalized Dirac operators on manifolds with cusps of rank one. This includes the case of spinor Laplacians on (XX)-rank one locally symmetric spaces. The time-dependent approach to scattering theory is taken to derive the main results about the spectral resolution of these operators. The second part of the book deals with the derivation of an index formula for generalized Dirac operators on manifolds with cusps of rank one. This index formula is used to prove a conjecture of Hirzebruch concerning the relation of signature defects of cusps of Hilbert modular varieties and special values of L-series. This book is intended for readers working in the field of automorphic forms and analysis on non-compact Riemannian manifolds, and assumes a knowledge of PDE, scattering theory and harmonic analysis on semisimple Lie groups. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1244 606 $aIndex theorems 615 0$aIndex theorems. 676 $a514.74 700 $aMu?ller$b Werner$f1949-$01221066 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466383803316 996 $aManifolds with cusps of rank one$92831084 997 $aUNISA