Elliptic Functions and Modular Forms

• Verfasst von: Koecher, Max [VerfasserIn]
• Verfasst von: Krieg, Aloys [VerfasserIn]
• Titel: Elliptic Functions and Modular Forms
• Verf.angabe: by Max Koecher, Aloys Krieg
• Ausgabe: 1st ed. 2025.
• Verlagsort: Berlin, Heidelberg
• Verlagsort: Berlin, Heidelberg
• Verlag: Springer Berlin Heidelberg
• Verlag: Imprint: Springer
• E-Jahr: 2025
• Jahr: 2025.
• Jahr: 2025.
• Umfang: 1 Online-Ressource(X, 362 p.)
• Gesamttitel/Reihe: Universitext
• ISBN: 978-3-662-71224-5
• DOI: doi:10.1007/978-3-662-71224-5
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• K10plus-PPN: 1924770938
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.

Abstract

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.