03130nam 2200685Ia 450 991077703200332120200520144314.01-281-93408-99786611934088981-279-237-6(CKB)1000000000411668(EBL)1679398(SSID)ssj0000169910(PQKBManifestationID)11165367(PQKBTitleCode)TC0000169910(PQKBWorkID)10215301(PQKB)10060211(MiAaPQ)EBC1679398(WSP)00006438(Au-PeEL)EBL1679398(CaPaEBR)ebr10255817(CaONFJC)MIL193408(OCoLC)879023565(PPN)168075628(EXLCZ)99100000000041166820070912d2008 uy 0engur|n|---|||||txtccrHecke's theory of modular forms and Dirichlet series[electronic resource] /Bruce C. Berndt, Marvin I. KnoppHacensack, NJ World Scientificc20081 online resource (150 p.)Monographs in Number TheoryExpanded version of lecture notes by B. Berndt based in turn on a series of lectures given by Erich Hecke in 1938.981-270-635-6 Includes bibliographical references (p. 129-134) and index.Preface 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; IndexIn 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 developmentsMonographs in Number TheoryDirichlet seriesForms (Mathematics)Modular functionsHecke operatorsDirichlet series.Forms (Mathematics)Modular functions.Hecke operators.515.243Berndt Bruce C.1939-54440Hecke Erich1887-1947.59032Knopp Marvin Isadore1933-60287MiAaPQMiAaPQMiAaPQBOOK9910777032003321Hecke's theory of modular forms and Dirichlet series3816082UNINA