Rank differences for overpartitions
数论
2021-02-03 v2 组合数学
摘要
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.
关键词
引用
@article{arxiv.math/0703326,
title = {Rank differences for overpartitions},
author = {Jeremy Lovejoy and Robert Osburn},
journal= {arXiv preprint arXiv:math/0703326},
year = {2021}
}
备注
17 pages, final version, accepted for publication in the Quarterly Journal of Mathematics