English

On some sums involving the counting function of non-isomorphic abelian groups

Number Theory 2022-04-07 v1

Abstract

Let a(n)a(n) denote the number of non-isomorphic abelian groups with nn elements. In 1991 Ivi\'{c} proved an asymptotic formula of the sum nxa(n+a(n)).\sum_{n\leq x} a(n+ a(n)). In this paper, we will prove a sharper asymptotic formula for this sum.

Keywords

Cite

@article{arxiv.2204.02576,
  title  = {On some sums involving the counting function of non-isomorphic abelian groups},
  author = {Haihong Fan and Wenguang Zhai},
  journal= {arXiv preprint arXiv:2204.02576},
  year   = {2022}
}