## Partitions, q-Series, and Modular FormsKrishnaswami Alladi, Frank Garvan 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

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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### Common terms and phrases

A(xq Amer applied asymptotic B.C. Berndt Bailey’s basic hypergeometric series Bringmann coefficients combinatorial congruences cosh ox cusp defined Department of Mathematics Developments in Mathematics Dominated Convergence Theorem G.E. Andrews harmonic Maass forms ižj Jackson integral Jśn linear London Math MacMahon Mathematics Subject Classification mf3s Milne mock theta conjectures mock theta functions modular forms modulo Mordell integrals multiple series multiple sums multivariate n-simplex nonnegative integers nonterminating notation number of partitions Number Theory obtain order mock theta paper parameters Partition Analysis partition function plane partitions polynomial positive integers Proc proof of Theorem proved pS(n q-SaalschØutz transformations q-series quintuple product identity qxi/xj R.J. McIntosh Ramanujan reduces Rogers-Ramanujan Rogers-Ramanujan identities root system roots of unity Sect sequences Springer Science+Business Media summation theorem Theorem 1.1 transformation formula transformation laws upper bound sum y1 yn yeNn zn curve Zwegers