LEADER 03130nam 2200685Ia 450 001 9910777032003321 005 20200520144314.0 010 $a1-281-93408-9 010 $a9786611934088 010 $a981-279-237-6 035 $a(CKB)1000000000411668 035 $a(EBL)1679398 035 $a(SSID)ssj0000169910 035 $a(PQKBManifestationID)11165367 035 $a(PQKBTitleCode)TC0000169910 035 $a(PQKBWorkID)10215301 035 $a(PQKB)10060211 035 $a(MiAaPQ)EBC1679398 035 $a(WSP)00006438 035 $a(Au-PeEL)EBL1679398 035 $a(CaPaEBR)ebr10255817 035 $a(CaONFJC)MIL193408 035 $a(OCoLC)879023565 035 $a(PPN)168075628 035 $a(EXLCZ)991000000000411668 100 $a20070912d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHecke's theory of modular forms and Dirichlet series$b[electronic resource] /$fBruce C. Berndt, Marvin I. Knopp 210 $aHacensack, NJ $cWorld Scientific$dc2008 215 $a1 online resource (150 p.) 225 1 $aMonographs in Number Theory 300 $aExpanded version of lecture notes by B. Berndt based in turn on a series of lectures given by Erich Hecke in 1938. 311 $a981-270-635-6 320 $aIncludes bibliographical references (p. 129-134) and index. 327 $aPreface in Two Acts with a Prelude, Interlude, and Postlude; Contents; 1. Introduction; 2. The main correspondence theorem; 3. A fundamental region; 4. The case > 2; 5. The case < 2; 6. The case = 2; 7. Bochner's generalization of the main correspondence theorem of Hecke, and related results; 8. Identities equivalent to the functional equation and to the modular relation; Bibliography; Index 330 $aIn 1938, at the Institute for Advanced Study, E Hecke gave a series of lectures on his theory of correspondence between modular forms and Dirichlet series. Since then, the Hecke correspondence has remained an active feature of number theory and, indeed, it is more important today than it was in 1936 when Hecke published his original papers. This book is an amplified and up-to-date version of the former author's lectures at the University of Illinois at Urbana-Champaign, based on Hecke's notes. Providing many details omitted from Hecke's notes, it includes various new and important developments 410 0$aMonographs in Number Theory 606 $aDirichlet series 606 $aForms (Mathematics) 606 $aModular functions 606 $aHecke operators 615 0$aDirichlet series. 615 0$aForms (Mathematics) 615 0$aModular functions. 615 0$aHecke operators. 676 $a515.243 700 $aBerndt$b Bruce C.$f1939-$054440 701 $aHecke$b Erich$f1887-1947.$059032 701 $aKnopp$b Marvin Isadore$f1933-$060287 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910777032003321 996 $aHecke's theory of modular forms and Dirichlet series$93816082 997 $aUNINA