Asymptotic behavior of the irrational factor

E. Alkan; A. H. Ledoan; A. Zaharescu

doi:10.1007/s10474-008-7212-9

Asymptotic behavior of the irrational factor

E. Alkan, A. H. Ledoan, A. Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the irrational factor function I(n) introduced by Atanassov and defined by I(n) = ∏_ν=1^k p_ν ^1/αν, where n = ∏_ν=1^k p _ν^1/αν is the prime factorization of n. We show that the sequence {G(n)/n} _n≧1, where G(n) = ∏ _ν=1ⁿ I(ν)^1/n , is convergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function I(n).

Original language	English (US)
Pages (from-to)	293-305
Number of pages	13
Journal	Acta Mathematica Hungarica
Volume	121
Issue number	3
DOIs	https://doi.org/10.1007/s10474-008-7212-9
State	Published - Nov 2008

Keywords

Arithmetic functions
Averages
Dirichlet series
Irrational factor
Riemann zeta-function

ASJC Scopus subject areas

Mathematics(all)

Online availability

10.1007/s10474-008-7212-9

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AB - We study the irrational factor function I(n) introduced by Atanassov and defined by I(n) = ∏ν=1k pν 1/αν, where n = ∏ν=1k p ν1/αν is the prime factorization of n. We show that the sequence {G(n)/n} n≧1, where G(n) = ∏ ν=1n I(ν)1/n , is convergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function I(n).

KW - Arithmetic functions

KW - Averages

KW - Dirichlet series

KW - Irrational factor

KW - Riemann zeta-function

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Asymptotic behavior of the irrational factor

Abstract

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