Rank differences for overpartitions
Number Theory
2021-02-03 v2 Combinatorics
Abstract
In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulas for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulas for the generating functions for rank differences for overpartitions. These are in terms of modular functions and generalized Lambert series.
Keywords
Cite
@article{arxiv.math/0703326,
title = {Rank differences for overpartitions},
author = {Jeremy Lovejoy and Robert Osburn},
journal= {arXiv preprint arXiv:math/0703326},
year = {2021}
}
Comments
17 pages, final version, accepted for publication in the Quarterly Journal of Mathematics