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On the Riesz means of δ k (n)

Abstract : Let k ≥ 1 be an integer. Let δ k (n) denote the maximum divisor of n which is co-prime to k. We study the error term of the general m-th Riesz mean of the arithmetical function δ k (n) for any positive integer m ≥ 1, namely the error term E m,k (x) where 1 m! n≤x δ k (n) 1 − n x m = M m,k (x) + E m,k (x). We establish a non-trivial upper bound for E m,k (x) , for any integer m ≥ 1.
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Saurabh Singh. On the Riesz means of δ k (n). Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2017, 40, pp.24 - 30. ⟨hal-01671230⟩

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