Riesz means of the Dedekind function II
Let $ψ$ denote the Dedekind totient function defined by $ ψ(n)=\sum_{d|n}dμ^2ł({n}/{d}\r) $ with $μ$ being the Möbius function. We shall consider the $k$-th Riesz mean of the arithmetical function $n/ψ(n)$ for any non-negative integer $k$ on the assumptions that the Riemann Hypothesis is true, and all the zeros $ρ$ on the critical line of the Riemann zeta function $ζ$ are simple. Our result is an explicit representation of the error term in the formula obtained in a previous work of the second author and I. Kiuchi \cite{IK}. We also give an improvement on the error estimate under the assumption of the Gonek-Hejhal Hypothesis. And, we propose a proposition that is equivalent to the Riemann Hypothesis.
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