Small values of the Euler function and the Riemann hypothesis
type: Item
instance of: scholarly article
title: Small values of the Euler function and the Riemann hypothesis
zbMATH Open document ID: 1272.11109
published in: Acta Arithmetica
publication date: 2012-10-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1202.0729
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11M26
Mathematics Subject Classification ID: 11N56
zbMATH DE Number: 6090471
zbMATH Keywords: Euler's function
zbMATH Keywords: Riemann hypothesis
author: Jean-Louis Nicolas
MaRDI profile type: Publication
OpenAlex ID: W2113680225
arXiv ID: 1202.0729
DOI: 10.4064/AA155-3-7
review text: The author studies the function NEWLINE\[NEWLINEc(n)= \Biggl({n\over\varphi(n)}- e^\gamma\log\log n\Biggr)\sqrt{\log n}.NEWLINE\]NEWLINE He proves that several explicit bounds for \(c(n)\) are equivalent to the Riemann hypothesis. One of these upper bounds is NEWLINE\[NEWLINEc(n)\leq c\Biggl(\prod_{1\leq k\leq 66} p_k\Biggr)= 4,06\dots;NEWLINE\]NEWLINE here \(p_1< p_2<\cdots\) denotes the series of primes.
reviewed by: Jürgen Spilker
description: scientific article; zbMATH DE number 6090471