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Partitions, q-Series, and Modular Forms

  • Book
  • © 2012

Overview

Editors:
  1. Krishnaswami Alladi

    1. , Department of Mathematics, University of Florida, Gainesville, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Frank Garvan

    1. , Mathematics, University of Florida, Gainesville, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Unique volume describing recent progress in the fields of q-hypergeometric series, partitions, and modular forms and their relation to number theory, combinatorics, and special functions
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  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
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Keywords

About this book

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.

Editors and Affiliations

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

    Krishnaswami Alladi

  • , Mathematics, University of Florida, Gainesville, USA

    Frank Garvan

About the editors

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.

Bibliographic Information

  • Book Title: Partitions, q-Series, and Modular Forms

  • Editors: Krishnaswami Alladi, Frank Garvan

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4614-0028-8

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC 2012

  • Hardcover ISBN: 978-1-4614-0027-1Published: 01 November 2011

  • Softcover ISBN: 978-1-4939-0186-9Published: 25 January 2014

  • eBook ISBN: 978-1-4614-0028-8Published: 01 November 2011

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: XII, 224

  • Topics: Number Theory, Combinatorics, Special Functions

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