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Beschreibung

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.

Inhaltsverzeichnis

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.

Details
Erscheinungsjahr: 2025
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: viii
364 S.
ISBN-13: 9783662712238
ISBN-10: 3662712237
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Krieg, Aloys
Koecher, Max
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
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: Aloys Krieg (u. a.)
Erscheinungsdatum: 02.05.2025
Gewicht: 0,631 kg
Artikel-ID: 132618113

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