1.

Record Nr.

UNINA9911001456503321

Autore

Koecher Max

Titolo

Elliptic Functions and Modular Forms / / by Max Koecher, Aloys Krieg

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2025

ISBN

3-662-71224-5

Edizione

[1st ed. 2025.]

Descrizione fisica

1 online resource (373 pages)

Collana

Universitext, , 2191-6675

Disciplina

516.9

Soggetti

Functions of complex variables

Number theory

Geometry, Hyperbolic

Group theory

Functions of a Complex Variable

Number Theory

Hyperbolic Geometry

Group Theory and Generalizations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.