Hecke's theory of modular forms and Dirichlet series
著者
書誌事項
Hecke's theory of modular forms and Dirichlet series
World Scientific, c2008
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注記
Expanded version of lecture notes by B. Berndt based in turn on a series of lectures given by Erich Hecke in 1938
Includes bibliographical references (p. 129-134) and index
内容説明・目次
内容説明
In 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 in recent years. In particular, several generalizations and analogues of the original Hecke theory are briefly described in this concise volume.
目次
- The Main Correspondence Theorem
- A Fundamental Region
- The Case > 2
- The Case < 2
- The Case = 2
- Bochner's Generalization of the Main Correspondence Theorem of Hecke and Related Results
- Identities Equivalent to the Functional Equation and to the Modular Relation.
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