Rank deviations for overpartitions
Number Theory
2025-07-14 v2 Combinatorics
Abstract
We prove general fomulas for the deviations of two overpartition ranks from the average. These formulas are in terms of Appell--Lerch series and sums of quotients of theta functions and can be used, among other things, to recover any of the numerous overpartition rank difference identities in the literature. We give two illustrations.
Cite
@article{arxiv.2307.03418,
title = {Rank deviations for overpartitions},
author = {Jeremy Lovejoy and Robert Osburn},
journal= {arXiv preprint arXiv:2307.03418},
year = {2025}
}
Comments
15 pages, to appear in Research in Number Theory