Robin inequality for n/phi(n)

Let $\varphi(n)$ be the Euler function, $\sigma(n)=\sum_{d\mid n}d$ the sum of divisors function and $\gamma=0.577\ldots$ the Euler constant. In 1982, Robin proved that, under the Riemann hypothesis, $\sigma(n)/n < e^\gamma \log\log n$ holds for $n > 5040$ and that this inequality is equivalen...

Full description

Saved in:
Bibliographic Details
Published in:New Zealand journal of mathematics 2024-05, Vol.55, p.1-9
Main Author: Nicolas, Jean-Louis
Format: Article
Language:English
Subjects:
Mathematics
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let $\varphi(n)$ be the Euler function, $\sigma(n)=\sum_{d\mid n}d$ the sum of divisors function and $\gamma=0.577\ldots$ the Euler constant. In 1982, Robin proved that, under the Riemann hypothesis, $\sigma(n)/n < e^\gamma \log\log n$ holds for $n > 5040$ and that this inequality is equivalent to the Riemann hypothesis. The aim of this paper is to give a similar equivalence for $n/\varphi(n)$.
ISSN:1179-4984
1171-6096
1179-4984
DOI:10.53733/324