English

Asymptotics of the counting function of $k$-th power-free elements in an arithmetic semigroup

Number Theory 2016-04-13 v1 Mathematical Physics math.MP

Abstract

For any k>1k>1, we find the asymptotics of the counting function of kk-th power-free elements in an additive arithmetic semigroup with exponential growth of the abstract prime counting function. This paper continues the authors' earlier research dealing with the case of infinite kk.

Keywords

Cite

@article{arxiv.1604.03509,
  title  = {Asymptotics of the counting function of $k$-th power-free elements in an arithmetic semigroup},
  author = {V. L. Chernyshev and D. S. Minenkov and V. E. Nazaikinskii},
  journal= {arXiv preprint arXiv:1604.03509},
  year   = {2016}
}