English

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 N(a,c,n), \overline{N}(a,c,n), the number of overpartitions of n n with rank congruent to a a modulo c, c, is equidistributed with respect to 0a<c, 0\le a< c, for any c2, c\ge2, as n n\to\infty and, in addition, we prove some inequalities between ranks of overpartitions conjectured by Ji, Zhang and Zhao (2018), and Wei and Zhang (2018) for n=6 n=6 and n=10. n=10.

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.}