Ranks of overpartitions: Asymptotics and inequalities
Number Theory
2019-10-01 v2
Abstract
In this paper we compute asymptotics for the coefficients of an infinite class of overpartition rank generating functions. Using these results, we show that the number of overpartitions of with rank congruent to modulo is equidistributed with respect to for any as and, in addition, we prove some inequalities between ranks of overpartitions conjectured by Ji, Zhang and Zhao (2018), and Wei and Zhang (2018) for and
Keywords
Cite
@article{arxiv.1904.07055,
title = {Ranks of overpartitions: Asymptotics and inequalities},
author = {Alexandru Ciolan},
journal= {arXiv preprint arXiv:1904.07055},
year = {2019}
}
Comments
23 pages; to appear in \textit{J. Math. Anal. Appl.}