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

3) ((1) National Research University Higher School of Economics; Dolgoprudny; D.S. Minenkov (2); Moscow; Moscow District; Russia); Russia (2) Ishlinsky Institute for Problems in Mechanics; Russia (3) Moscow Institute of Physics; Russian Academy of Sciences; Technology (State University)

arxiv: 1604.03509 · v1 · pith:ZMSPCRREnew · submitted 2016-04-09 · 🧮 math.NT · math-ph· math.MP

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

V.L. Chernyshev (1) , D.S. Minenkov (2) , V.E. Nazaikinskii (2 , 3) ((1) National Research University Higher School of Economics , Moscow , Russia (2) Ishlinsky Institute for Problems in Mechanics , Russian Academy of Sciences , Russia (3) Moscow Institute of Physics

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Technology (State University) Dolgoprudny Moscow District Russia)

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keywords countingfunctionarithmeticasymptoticselementspower-freesemigroupabstract

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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 $k$.

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

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