Modular Forms and Hecke Operators
1995
American Mathematical Society (Verlag)
978-0-8218-0277-9 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-0277-9 (ISBN)
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The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. This book explains the status of the theory of Hecke operators on spaces of holomorphic modular forms of integer.
The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results.The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups. Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results.The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups. Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
Introduction Theta-series Modular forms Hecke rings Hecke operators Symmetric matrices over a field Quadratic spaces Modules in quadratic fields and binary quadratic forms Notes References List of notation.
| Erscheint lt. Verlag | 30.8.1995 |
|---|---|
| Reihe/Serie | Translations of Mathematical Monographs |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 822 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 0-8218-0277-1 / 0821802771 |
| ISBN-13 | 978-0-8218-0277-9 / 9780821802779 |
| Zustand | Neuware |
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