For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who revised it substantially for the English edition. It sets out to provide the reader with the basic knowledge of elliptic modular forms necessary to understand the recent developments in number theory. The first part gives the general theory of modular groups, modular forms and Hecke operators, with emphasis on the Hecke-Weil theory of the relation between modular forms and Dirichlet series. The second part is on the unit groups of quaternion algebras, which are seldom dealt with in books. The so-called Eichler-Selberg trace formula of Hecke operators follows next and the explicit computable formula is given. In the last chapter, written for the English edition, Eisenstein series with parameter are discussed following the recent work of Shimura: Eisenstein series are likely to play a very important role in the future progress of number theory, and thischapter provides a good introduction to the topic.
| ISBN: | 9783540295921 |
| Publication date: | 7th December 2005 |
| Author: | Toshitsune Miyake |
| Publisher: | Springer an imprint of Springer Berlin Heidelberg |
| Format: | Hardback |
| Pagination: | 338 pages |
| Series: | Springer Monographs in Mathematics |
| Genres: |
Number theory Algebraic geometry |
For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who revised it substantially for the English edition. It sets out to provide the reader with the basic knowledge of elliptic modular forms necessary to understand the recent developments in number theory. The first part gives the general theory of modular groups, modular forms and Hecke operators, with emphasis on the Hecke-Weil theory of the relation between modular forms and Dirichlet series. The second part is on the unit groups of quaternion algebras, which are seldom dealt with in books. The so-called Eichler-Selberg trace formula of Hecke operators follows next and the explicit computable formula is given. In the last chapter, written for the English edition, Eisenstein series with parameter are discussed following the recent work of Shimura: Eisenstein series are likely to play a very important role in the future progress of number theory, and thischapter provides a good introduction to the topic.
Modular Forms features in the following genres: Number theory, Algebraic geometry
Modular Forms is available in Hardback
Modular Forms was written by Toshitsune Miyake and published by Springer an imprint of Springer Berlin Heidelberg
Modular Forms has 338 pages
Yes it is part of Springer Monographs in Mathematics series