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Partitions, q-series, and modular forms

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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.

Author(s): George E. Andrews, Peter Paule (auth.), Krishnaswami Alladi, Frank Garvan (eds.)
Series: Developments in Mathematics volume 23
Edition: 1
Publisher: Springer-Verlag New York
Year: 2012

Language: English
Pages: 224
Tags: Number Theory; Combinatorics; Special Functions

Front Matter....Pages i-xii
MacMahon’s Dream....Pages 1-12
Ramanujan’s Elementary Method in Partition Congruences....Pages 13-21
Coefficients of Harmonic Maass Forms....Pages 23-38
On the Growth of Restricted Integer Partition Functions....Pages 39-46
On Applications of Roots of Unity to Product Identities....Pages 47-52
Lecture Hall Sequences, q -Series, and Asymmetric Partition Identities....Pages 53-68
Generalizations of Hutchinson’s Curve and the Thomae Formulae....Pages 69-81
On the Parity of the Rogers-Ramanujan Coefficients....Pages 83-93
A Survey of Classical Mock Theta Functions....Pages 95-144
An Application of Cauchy–Sylvester’s Theorem on Compound Determinants to a BC n -Type Jackson Integral....Pages 145-157
Multiple Generalizations of q -Series Identities and Related Formulas....Pages 159-180
Nonterminating q-Whipple Transformations for Basic Hypergeometric Series in U(n)....Pages 181-224