RIESZ MEANS OF THE DEDEKIND FUNCTION

Abstract

Let ψ denote the Dedekind totient function by id ∗ μ², where μ is the Möbius function. We establish the asymptotic formula of the general kth Riesz mean of the arithmetical function n/ψ(n) for any positive integer k ≥ 2; namely

Assuming that the Riemann Hypothesis is true, then the error term of the above function can be estimated as O(k⁻¹x^−1/2+δ) for any small positive constant δ.