On sums of logarithmic averages of gcd-sum functions

2018/04/05 by Isao Kiuchi, Kiuchi, Isao, Sumaia Saad Eddin +1
Mathematics · Social Sciences · #11A25 #11N37 #11Y60 #Analytic Number Theory Research #FOS: Mathematics #Historical Geopolitical and Social Dynamics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1804.01902

openalex publication_date 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let gcd(k,j) be the greatest common divisor of the integers k and j. For any arithmetical function f, we establish several asymptotic formulas for weighted averages of gcd-sum functions with weight concerning logarithms, that is ∑_{k≤ x}(1)/(k) ∑_j=1^kf(gcd(k,j)) log j. More precisely, we give asymptotic formulas for various multiplicative functions such as f=id, ϕ, id_1+a and ϕ_1+a with -1

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