Asymptotics of the counting function of $k$-th power-free elements in an   arithmetic semigroup
  For any $k>1$, we find the asymptotics of the counting function of $k$-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 $k$. 
V.L. Chernyshev (1), D.S. Minenkov (2), V.E. Nazaikinskii (2 and 3)   ((1) National Research University Higher School of Eco...
math.NT math-ph math.MP