On a sum involving the Möbius function

I. Kiuchi, M. Minamide, and Y. Tanigawa. "On a sum involving the Möbius function." Acta Arithmetica 169.2 (2015): 149-168. <http://eudml.org/doc/278953>.

@article{I2015,
abstract = {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 $ĉ_\{q\}(n) := ∑_\{d|(q,n)\}d|μ(q/d)|$.},
author = {I. Kiuchi, M. Minamide, Y. Tanigawa},
journal = {Acta Arithmetica},
keywords = {ramanujan's sum; Möbius function; asymptotic formulas},
language = {eng},
number = {2},
pages = {149-168},
title = {On a sum involving the Möbius function},
url = {http://eudml.org/doc/278953},
volume = {169},
year = {2015},
}

TY - JOUR
AU - I. Kiuchi
AU - M. Minamide
AU - Y. Tanigawa
TI - On a sum involving the Möbius function
JO - Acta Arithmetica
PY - 2015
VL - 169
IS - 2
SP - 149
EP - 168
AB - 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 $ĉ_{q}(n) := ∑_{d|(q,n)}d|μ(q/d)|$.
LA - eng
KW - ramanujan's sum; Möbius function; asymptotic formulas
UR - http://eudml.org/doc/278953
ER -