Partitions, q-Series, and Modular Forms

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Krishnaswami Alladi, Frank Garvan
Springer Science & Business Media, Nov 2, 2011 - Mathematics - 224 pages
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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.
 

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Contents

MacMahons Dream
1
Ramanujans Elementary Method in Partition Congruences
13
Coefficients of Harmonic Maass Forms
23
On the Growth of Restricted Integer Partition Functions
39
On Applications of Roots of Unity to Product Identities
47
Lecture Hall Sequences qSeries and Asymmetric Partition Identities
53
Generalizations of Hutchinsons Curve and the Thomae Formulae
69
On the Parity of the RogersRamanujan Coefficients
82
A Survey of Classical Mock Theta Functions
95
An Application of CauchySylvesters Theorem on Compound Determinants to a BCnType Jackson Integral
145
Multiple Generalizations of qSeries Identities and Related Formulas
158
Nonterminating qWhipple Transformations for Basic Hypergeometric Series in Un
181
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About the author (2011)

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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