Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-01671230v1

Volume: Volume 40

Published on: January 11, 2018

Submitted on: October 5, 2016

Keywords: Euler-totient function,Riemann zeta-function ,Generating functions,2010 Mathematics Subject Classification Primary 11A25, Secondary 11N37.,
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Mathematics [math]

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