Some asymptotic formulae involving Cohen-Ramanujan expansions

Arya Chandran, Vishnu Namboothiri K

Cohen-Ramanujan sum, denoted by $c_r^s(n)$, is an exponential sum similar to the Ramanujan sum $c_r(n):=\sum _{\begin{array}{c}h=1\\ (h,r)=1\end{array}}^r{e}^{\frac{2\pi inh}{r}}$. An arithm…