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

数学科目

研究成果: Article › 査読

4 被引用数 (Scopus)

抄録

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.

本文言語	English
論文番号	16.2.7
ジャーナル	Journal of Integer Sequences
巻	19
号	2
出版ステータス	Published - 2016 3月 18

ASJC Scopus subject areas

離散数学と組合せ数学

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引用スタイル

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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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SN - 1530-7638

VL - 19

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

IS - 2

M1 - 16.2.7

ER -

Sums of products of generalized Ramanujan sums

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ASJC Scopus subject areas

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