Singh, Saurabh Kumar - On the Riesz means of $\delta_k(n)$

hrj:2058 - Hardy-Ramanujan Journal, January 11, 2018, Volume 40
On the Riesz means of $\delta_k(n)$

Authors: Singh, Saurabh Kumar

Let $k\geq 1$ be an integer. Let $\delta_k(n)$ 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 $\delta_k(n)$ for any positive integer $m \ge 1$, namely the error term $E_m(x)$ where \[ \frac{1}{m!}\sum_{n \leq x}\delta_k(n) \left( 1-\frac{n}{x} \right)^m = M_{m, k}(x) + E_{m, k}(x). \] We establish a non-trivial upper bound for $\left | E_{m, k} (x) \right |$, for any integer $m\geq 1$.


Source : oai:arXiv.org:1609.06184
Volume: Volume 40
Published on: January 11, 2018
Submitted on: October 5, 2016
Keywords: Mathematics - Number Theory


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