Partitions, q-Series, and Modular Forms

  • Krishnaswami Alladi
  • Frank Garvan

Part of the Developments in Mathematics book series (DEVM, volume 23)

Table of contents

  1. Front Matter
    Pages i-xii
  2. George E. Andrews, Peter Paule
    Pages 1-12
  3. Bruce C. Berndt, Chadwick Gugg, Sun Kim
    Pages 13-21
  4. Kathrin Bringmann, Ken Ono
    Pages 23-38
  5. E. Rodney Canfield, Herbert S. Wilf
    Pages 39-46
  6. Sylvie Corteel, Carla D. Savage, Andrew V. Sills
    Pages 53-68
  7. Basil Gordon, Richard J. McIntosh
    Pages 95-144

About this book

Introduction

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.

A common theme in the book is the study of q-series, an area which in recent years has witnessed dramatic advances having significant impact on a variety of fields within and outside of mathematics such as physics. Most major aspects of the modern theory of q-series and how they relate to number theory, combinatorics, and special functions are represented in this volume. Topics include the theory of partitions via computer algebra, elementary asymptotic methods; expositions on Ramanujan's mock theta-functions emphasizing the classical aspects as well as the recent exciting connections with the theory of harmonic Maass forms; congruences for modular forms; a study of theta-functions from elementary, function-theoretic and Riemann surface viewpoints; and a systematic analysis of multiple basic hypergeometric functions associated with root systems of Lie algebras.

 The broad range of topics covered in this volume will be of interest to both researchers and graduate students who want to learn of recent developments in the theory of partitions, q-series and modular forms and their far reaching impact on diverse areas of mathematics.

Keywords

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

Editors and affiliations

  • Krishnaswami Alladi
    • 1
  • Frank Garvan
    • 2
  1. 1., Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2., MathematicsUniversity of FloridaGainesvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-0028-8
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-0027-1
  • Online ISBN 978-1-4614-0028-8
  • Series Print ISSN 1389-2177
  • About this book