Problems in the Theory of Modular Forms (Imsc Lecture Notes in Mathematics)

Murty, M. Ram/ Dewar, Michael/ Graves, Hester

Hindustan Book Agency（2016/12発売）

• 製本 Hardcover:ハードカバー版
• 言語 ENG
• 商品コード 9789811026508
• DDC分類 512

Full Description

This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan tau-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.

Contents

Part I Problems.- Chapter 1. Jacobi's q-series.- Chapter 2. The Modular Group.- Chapter 3. The Upper Half-Plane.- Chapter 4. Modular Forms of Level One.- Chapter 5. The Ramanujan _ T-function.- Chapter 6. Modular Forms of Higher Level.- Chapter 7. The Petersson Inner Product.- Chapter 8. Hecke Operators of Higher Level.- Chapter 9. Dirichlet Series and Modular Forms.- Chapter 10. Special Topics.- Part II Solutions.- Chapter 1. Jacobi's q-series.- Chapter 2. The Modular Group.- Chapter 3. The Upper Half-Plane.- Chapter 4. Modular Forms of Level One.- Chapter 5. The Ramanujan _ T-function.- Chapter 6. Modular Forms of Higher Level.- Chapter 7. The Petersson Inner Product.- Chapter 8. Hecke Operators of Higher Level.- Chapter 9. Dirichlet Series and Modular Forms.- Chapter 10. Special Topics.