Some asymptotic formulae involving Cohen-Ramanujan expansions
Some asymptotic formulae involving Cohen-Ramanujan expansions
Cohen-Ramanujan sum, denoted by $c_r^s(n)$, is an exponential sum similar to the Ramanujan sum $c_r(n):=\sum\limits_{\substack{h=1\\{(h,r)=1}}}^{r}e^{\frac{2\pi i n h}{r}}$. An arithmetical function $f$ is said to admit a Cohen-Ramanujan expansion $ f(n):=\sum\limits_{r}\widehat{f}(r)c_r^s(n)$ if the series on the right hand side converges for suitable complex numbers $\widehat{f}(r)$. Given two arithmetical functions $f$ …