Partitions, q-Series, and Modular Forms

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 conference has led to annual year-long programs in Algebra, Number Theory, and Combinatorics (ANTC) at the university. The broad coverage of the works in this volume will be of interest to researchers and graduate students who want to learn of recent developments in the theory of q-series and modular forms and how it relates to number theory, combinatorics, and special functions.

-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).