1Department of Mathematical Sciences Faculty of Science Yamaguchi University Yoshida 1677-1 Yamaguchi 753-8512, Japan 2Graduate School of Mathematics Nagoya University Nagoya 464-8602, Japan
Acta Arithmetica, Tome 169 (2015) no. 2, pp. 149-168
Let $c_{q}(n)$ be the Ramanujan sum, i.e. $c_{q}(n)=\sum_{d|(q,n)}d \mu(q/d)$, where $\mu$ is the Möbius function. In a paper of
Chan and Kumchev (2012), asymptotic formulas for $\sum_{n\leq y}(\sum_{q\leq x}c_{q}(n))^{k}$ ($k=1,2$) are obtained.
As an analogous problem, we evaluate $\sum_{n\leq y}(\sum_{n\leq x}\widehat{c}_{q}(n))^{k}$ ($k=1,2$),
where $\widehat{c}_{q}(n):=\sum_{d|(q,n)}d|\mu(q/d)|$.
Keywords:
ramanujan sum sum where bius function paper chan kumchev asymptotic formulas sum leq sum leq obtained analogous problem evaluate sum leq sum leq widehat where widehat sum
Affiliations des auteurs :
I. Kiuchi
1
;
M. Minamide
1
;
Y. Tanigawa
2
1
Department of Mathematical Sciences Faculty of Science Yamaguchi University Yoshida 1677-1 Yamaguchi 753-8512, Japan
2
Graduate School of Mathematics Nagoya University Nagoya 464-8602, Japan
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author = {I. Kiuchi and M. Minamide and Y. Tanigawa},
title = {On a sum involving the {M\"obius} function},
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I. Kiuchi; M. Minamide; Y. Tanigawa. On a sum involving the Möbius function. Acta Arithmetica, Tome 169 (2015) no. 2, pp. 149-168. doi: 10.4064/aa169-2-3
