Elliptic Functions and Modular Forms by Max Koecher, Aloys Krieg - 9783662712238

Elliptic Functions and Modular FormsAuthor(s): Max Koecher, Aloys Krieg\nFormat: Paperback\nPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Germany\nImprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K\nISBN-13: 9783662712238, 978-3662712238\nSynopsis\nThe 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 Weierstrasss 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.