Partitions, q-Series, and Modular Forms

• Corporate Author: SpringerLink (Online service)
• Other Authors: Alladi, Krishnaswami (Editor), Garvan, Frank (Editor)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2012.
• Series: Developments in Mathematics, 23
• Subjects: Mathematics.; Special functions.; Number theory.; Combinatorics.; Number Theory.; Special Functions.

This book contains a unique collection of both research and survey papers written by an international group of some of the world's experts on partitions, q-series, and modular forms, as outgrowths of a conference held at the University of Florida, Gainesville in March 2008. The success of this...

Table of Contents:

• -Preface (K. Alladi and F. Garvan)
• 1. MacMahon's dream (G. E. Andrews and P. Paule)
• 2. Ramanujan's elementary method in partition congruences (B. Berndt, C. Gugg, and S. Kim)
• 3. Coefficients of harmonic Maass forms (K. Bringmann and K. Ono)
• 4. On the growth of restricted partition functions (E. R. Canfield and H. Wilf)
• 5. On applications of roots of unity to product identities (Z. Cao)
• 6. Lecture hall sequences, q-series, and asymmetric partition identities (S. Corteel, C. Savage and A. Sills)
• 7. Generalizations of Hutchinson's curve and the Thomae formula (H. Farkas)
• 8. On the parity of the Rogers-Ramanujan coefficients (B. Gordon)
• 9. A survey of the classical mock theta functions (B. Gordon and R. McIntosh)
• 10. An application of the Cauchy-Sylvester theorem on compound determinants to a BC_n Jackson integral (M. Ito and S. Okada)
• 11. Multiple generalizations of q-series identities found in Ramanujan's Lost Notebook (Y. Kajihara)
• 12. Non-terminating q-Whipple transformations for basic hypergeometric series in U(n) (S. C. Milne and J. W. Newcomb).            .