Skip Navigation


The Quarterly Journal of Mathematics Advance Access originally published online on January 7, 2008
The Quarterly Journal of Mathematics 2008 59(2):257-273; doi:10.1093/qmath/ham031
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
59/2/257    most recent
ham031v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Lovejoy, J.
Right arrow Articles by Osburn, R.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

RANK DIFFERENCES FOR OVERPARTITIONS

Jeremy Lovejoy{dagger}

CNRS, LIAFA, Université Denis Diderot, 2, Place Jussieu, Case 7014, F-75251 Paris Cedex 05, France

Robert Osburn {ddagger}

School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
IHÉS, Le Bois-Marie, 35, Route de Chartres, F-91440 Bures-sur-Yvette, France

{dagger} Corresponding author. E-mail: lovejoy{at}liafa.jussieu.fr

Received 23 March 2007;
  Abstract

In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulae for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulae for the generating functions for rank differences for overpartitions. These are in terms of modular functions and generalized Lambert series.

{ddagger} E-mail: robert.osburn{at}ucd.ie; osburn{at}ihes.fr


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.