The Error Term of the Summatory Euler Phi Function

N. A. Carella

The Error Term of the Summatory Euler Phi Function

General Mathematics 2017-07-27 v5

Authors: N. A. Carella

Abstract

A sharper estimate for the summatory Euler phi function $\sum_{n \leq x} \varphi(n)$ is presented in this work. It improves the established estimate in the current mathematical literature. In addition, an estimate for its reciprocal $\sum_{n \leq x} 1/\varphi(n)$ is also determined.

Keywords

multiplicative functions exponential sums

Cite

@article{arxiv.1206.2792,
  title  = {The Error Term of the Summatory Euler Phi Function},
  author = {N. A. Carella},
  journal= {arXiv preprint arXiv:1206.2792},
  year   = {2017}
}

Comments

Sixteen Pages. Keywords: Euler Totient Function, Error Term, Arithmetic Function

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