Let ϕ(n) denote the Euler-totient function. We study the error term of the general k-th Riesz mean of the arithmetical function nϕ(n) for any positive integer k≥1, namely the error term Ek(x) where1k!∑n≤xnϕ(n)(1−nx)k=Mk(x)+Ek(x).
The upper bound for |Ek(x)| established here thus improves the earlier known upper bound when k=1.
A. Kaur;A. Sankaranarayanan, 2023, On the Rankin–Selberg L-function related to the Godement–Jacquet L-function, Acta Mathematica Academiae Scientiarum Hungaricae, 169, 1, pp. 88-107, 10.1007/s10474-023-01296-9.