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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.
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.
Aloys Krieg (born 1955) studied mathematics at the University of Münster. He was the last PhD student of Max Koecher. He has mainly worked on modular forms of several variables. In 1993, he was appointed to Paul Butzer's chair at RWTH Aachen University, where he served as Vice President for Education for 16 years. He retired in 2024.
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.
| Erscheinungsjahr: | 2025 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Universitext |
| Inhalt: |
viii
364 S. |
| ISBN-13: | 9783662712238 |
| ISBN-10: | 3662712237 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Koecher, Max
Krieg, Aloys |
| Hersteller: |
Springer
Springer-Verlag GmbH Universitext |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 19 mm |
| Von/Mit: | Max Koecher (u. a.) |
| Erscheinungsdatum: | 02.05.2025 |
| Gewicht: | 0,631 kg |
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