On a sum involving certain arithmetic functions and the integral part function

Jing Ma; Huayan Sun

On a sum involving certain arithmetic functions and the integral part function

Number Theory 2021-09-08 v1

Authors: Jing Ma , Huayan Sun

Abstract

In this short, we study sums of the shape $\sum_{n\leqslant x}{f([x/n])}/{[x/n]},$ where $f$ is Euler totient function $\varphi$ , Dedekind function $\Psi$ , sum-of-divisors function $\sigma$ or the alternating sum-of-divisors function $\beta.$ We improve previous results when $f=\varphi$ and derive new estimates when $f=\Psi, f=\sigma$ and $f=\beta.$

Keywords

multiplicative functions exponential sums divisor function

Cite

@article{arxiv.2109.02924,
  title  = {On a sum involving certain arithmetic functions and the integral part function},
  author = {Jing Ma and Huayan Sun},
  journal= {arXiv preprint arXiv:2109.02924},
  year   = {2021}
}

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7 pages

On a sum involving certain arithmetic functions and the integral part function

Abstract

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