Asymptotic formula for the $M_2$-ranks of overpartitions

Helen W. J. Zhang; Ying Zhong

Asymptotic formula for the $M_2$-ranks of overpartitions

Combinatorics 2022-06-07 v1 Number Theory

Authors: Helen W. J. Zhang , Ying Zhong

Abstract

Let $\overline{N}_2(a,c,n)$ be the number of overpartitions of $n$ whose the $M_2$ -rank is congruent to $a$ modulo $c$ . In this paper, we obtain the asymptotic formula of $\overline{N}_2(a,c,n)$ utilizing the Ingham Tauberian Theorem. As applications, we derive inequalities concerning with $\overline{N}_2(a,c,n)$ including its strict concavity and log-concavity.

Keywords

overpartitions m2-rank asymptotic formula ingham tauberian theorem strict concavity log-concavity

Cite

@article{arxiv.2206.02167,
  title  = {Asymptotic formula for the $M_2$-ranks of overpartitions},
  author = {Helen W. J. Zhang and Ying Zhong},
  journal= {arXiv preprint arXiv:2206.02167},
  year   = {2022}
}

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