Modular Forms: A Classical and Computational Introduction (Google eBook)

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Imperial College Press, Aug 11, 2008 - MATHEMATICS - 224 pages
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This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat's last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it.
  

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Contents

1 Historical overview
5
2 Introduction to modular forms
11
3 Results on finitedimensionality
41
4 The arithmetic of modular forms
57
5 Applications of modular forms
93
6 Modular forms in characteristic p
143
7 Computing with modular forms
163
Appendix A Magma code for classical modular forms
195
Appendix B Sage code for classical modular forms
197
Appendix C Hints and answers to selected exercises
199
Bibliography
205
List of Symbols
217
Index
221
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