On a sum involving the Möbius function

• Autorzy: I. Kiuchi , M. Minamide , Y. Tanigawa
• Języki publikacji: EN

Abstrakty

EN

Let $c_{q}(n)$ be the Ramanujan sum, i.e. $c_{q}(n) = ∑_{d|(q,n)} dμ(q/d)$, where μ is the Möbius function. In a paper of Chan and Kumchev (2012), asymptotic formulas for $∑_{n≤y}(∑_{q≤x} c_{q}(n))^{k}$ (k = 1,2) are obtained. As an analogous problem, we evaluate $∑_{n≤y}(∑_{n≤x} ĉ_{q}(n))^{k}$ (k = 1,2), where $ĉ_{q}(n) := ∑_{d|(q,n)}d|μ(q/d)|$.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11L03: Trigonometric and exponential sums, general

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 169
• Numer: 2
• Strony: 149-168

Daty

wydano

2015

Twórcy

autor

I. Kiuchi

• Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, Japan

autor

M. Minamide

• Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, Japan

autor

Y. Tanigawa

• Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

Identyfikatory

DOI

10.4064/aa169-2-3