Ramanujan's Theta Functions

• Main Author: Cooper, Shaun (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Subjects: Mathematics.; Algebraic geometry.; Number theory.; Number Theory.; Algebraic Geometry.

Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12....

Table of Contents:

• Preface
• 0. Sum to Product Identities
• 1. Elliptic Functions
• 2. Transformations
• 3. Theta Functions
• 4. Levels 1, 2, 3, and 4: Jacobi's Inversion Theorem and Ramanujan's Alternative Theories
• 5. Level 5: The Rogers-Ramanujan Continued Fraction
• 6. Level 6: Ramanujan's Cubic Continued Fraction
• 7. Level 7
• 8. Level 8: The Ramanujan-Gollnitz-Gordon Continued Fraction
• 9. Level 9
• 10. Level 10: Ramanujan's Function k
• 11. Levels 11 and 23
• 12. Level 12
• 13. Hypergeometric Modular Transformations
• 14. Ramanujan's Series for 1/pi
• References.