Riesz means of the Euler totient function

Abstract

Let $\phi$ denote the Euler totient function, defined by $id*\mu$ where $\mu$ is the M\"{o}bius function. We shall consider the $k$-th Riesz mean of the arithmetical function $n/\phi(n)$ for any positive integer $k \geq 2$ on the assumption of the Riemann Hypothesis. Our result is a refinement of Theorem 2 in A. Sankaranarayanan and S.K. Singh [6]. We also improve it upon the assumption of the Gonek-Hejhal Hypothesis.