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arXiv · 1609.06184

On the Riesz means of $\delta_k(n)$

Saurabh Kumar Singh
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Abstract

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 $m\geq 1$.

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Saurabh Kumar Singh. 2016-09-20. On the Riesz means of $\delta_k(n)$. https://arxiv.org/abs/1609.06184

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