Elliptic Functions and Modular Forms
Series: Universitext;
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Product details:
- Publisher Springer Berlin Heidelberg
- Date of Publication 2 May 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783662712238
- Binding Paperback
- No. of pages364 pages
- Size 235x155 mm
- Language English
- Illustrations VIII, 364 p. Illustrations, black & white 658
Categories
Long description:
The theory of elliptic functions and modular forms is rich and storied, though it has a reputation for difficulty. In this textbook, the authors successfully bridge foundational concepts and advanced material. Following Weierstrass’s approach to elliptic functions, they also cover elliptic curves and complex multiplication. The sections on modular forms, which can be read independently, include discussions of Hecke operators and Dirichlet series. Special emphasis is placed on theta series, with some advanced results included. With detailed proofs and numerous exercises, this book is well-suited for self-study or use as a reference. A companion website provides videos and a discussion forum on the topic.
MoreTable of Contents:
1 Elliptic functions.- 2 Geometry in the upper-half plane and the action of the modular group.- 3 Modular forms.- 4 The Hecke-Petersson theory.- 5 Theta series.
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