Partitions, q-Series, and Modular Forms

1. Front Matter

   Pages i-xii

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2. MacMahon’s Dream

   • George E. Andrews, Peter Paule

   Pages 1-12

3. Ramanujan’s Elementary Method in Partition Congruences

   • Bruce C. Berndt, Chadwick Gugg, Sun Kim

   Pages 13-21

4. Coefficients of Harmonic Maass Forms

   • Kathrin Bringmann, Ken Ono

   Pages 23-38

5. On the Growth of Restricted Integer Partition Functions

   • E. Rodney Canfield, Herbert S. Wilf

   Pages 39-46

6. On Applications of Roots of Unity to Product Identities

   • Zhu Cao

   Pages 47-52

7. Lecture Hall Sequences, q-Series, and Asymmetric Partition Identities

   • Sylvie Corteel, Carla D. Savage, Andrew V. Sills

   Pages 53-68

8. Generalizations of Hutchinson’s Curve and the Thomae Formulae

   • Hershel M. Farkas

   Pages 69-81

9. On the Parity of the Rogers-Ramanujan Coefficients

   • Basil Gordon

   Pages 83-93

10. A Survey of Classical Mock Theta Functions

    • Basil Gordon, Richard J. McIntosh

    Pages 95-144

11. An Application of Cauchy–Sylvester’s Theorem on Compound Determinants to a BC _n -Type Jackson Integral

    • Masahiko Ito, Soichi Okada

    Pages 145-157

12. Multiple Generalizations of q-Series Identities and Related Formulas

    • Yasushi Kajihara

    Pages 159-180

13. Nonterminating q-Whipple Transformations for Basic Hypergeometric Series in U(n)

    • Stephen C. Milne, John W. Newcomb

    Pages 181-224

Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.

• basic hypergeometric series
• mock theta function
• modular forms
• partition function
• special functions
• combinatorics

• , Department of Mathematics, University of Florida, Gainesville, USA

  Krishnaswami Alladi

• , Mathematics, University of Florida, Gainesville, USA

  Frank Garvan

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.

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