Problems in the Theory of Modular Forms / by M. Ram Murty, Michael Dewar, Hester Graves.

Format:

Book

Author/Creator:

Murty, M. Ram., Author.

Dewar, Michael., Author.

Graves, Hester., Author.

Series:

IMSc Lecture Notes in Mathematics, 2509-808X

Language:

English

Subjects (All):

Number theory.

Operator theory.

Functions, Special.

Sequences (Mathematics).

Number Theory.

Operator Theory.

Special Functions.

Sequences, Series, Summability.

Local Subjects:

Number Theory.

Operator Theory.

Special Functions.

Sequences, Series, Summability.

Physical Description:

1 online resource (XVII, 291 p. 8 illus.)

Edition:

1st ed. 2016.

Place of Publication:

Singapore : Springer Singapore : Imprint: Springer, 2016.

Summary:

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 τ-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 10. Special Topics.

Notes:

Includes bibliographical references at the end of each chapters and index.

ISBN:

981-10-2651-3