Problems in the Theory of Modular Forms

• Main Authors: Murty, M. Ram (Author), Dewar, Michael (Author), Graves, Hester (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2016.
• Series: HBA Lecture Notes in Mathematics,
• Subjects: Mathematics.; Operator theory.; Sequences (Mathematics).; Special functions.; Number theory.; Number Theory.; Operator Theory.; Special Functions.; Sequences, Series, Summability.

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-pla...

Table of 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.