Sums of products of generalized Ramanujan sums

Soichi Ikeda; Isao Kiuchi; Kaneaki Matsuoka

Sums of products of generalized Ramanujan sums

Soichi Ikeda, Isao Kiuchi, Kaneaki Matsuoka

Department of Mathematics

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

5 Citations (Scopus)

Abstract

We consider weighted averages for the products t⁽¹⁾ _k1 (j) … t⁽ⁿ⁾ _kn (j) of generalized Ramanujan sums t⁽ⁱ⁾ _ki (j) = ∑_{d| gcd(ki, j)} f_i(d)g_i(k_i/d)h_i(j/d) with any arithmetical functions f_i, g_i and h_i (i = 1, …, n), and derive formulas for several weighted averages with weights concerning completely multiplicative functions, completely additive functions, and others.

Original language	English
Article number	16.2.7
Journal	Journal of Integer Sequences
Volume	19
Issue number	2
Publication status	Published - 2016 Mar 18

Keywords

Arithmetical function
Greatest common divisor
Ramanujan’s sum

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

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AU - Kiuchi, Isao

AU - Matsuoka, Kaneaki

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N2 - We consider weighted averages for the products t(1) k1 (j) … t(n) kn (j) of generalized Ramanujan sums t(i) ki (j) = ∑d| gcd(ki, j) fi(d)gi(ki/d)hi(j/d) with any arithmetical functions fi, gi and hi (i = 1, …, n), and derive formulas for several weighted averages with weights concerning completely multiplicative functions, completely additive functions, and others.

AB - We consider weighted averages for the products t(1) k1 (j) … t(n) kn (j) of generalized Ramanujan sums t(i) ki (j) = ∑d| gcd(ki, j) fi(d)gi(ki/d)hi(j/d) with any arithmetical functions fi, gi and hi (i = 1, …, n), and derive formulas for several weighted averages with weights concerning completely multiplicative functions, completely additive functions, and others.

KW - Arithmetical function

KW - Greatest common divisor

KW - Ramanujan’s sum

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ER -

Sums of products of generalized Ramanujan sums

Abstract

Keywords

ASJC Scopus subject areas

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