On Sums of Averages of Generalized Ramanujan Sums

Abstract

We shall consider some formulas for weighted averages of the generalized Ramanujan sum $\sum_{d|\gcd(k,n)}f(d)g\left({k}/{d}\right)h\left({n}/{d}\right)$ for any arithmetical functions $f,\ g$ and $h$, with the weights concerning completely multiplicative functions, completely additive functions and others.

Locations

• Project Euclid (Cornell University) - View - PDF
• Tokyo Journal of Mathematics - View