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 , we find the asymptotics of the counting function of -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 .
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}
}