Small values of the Euler function and the Riemann hypothesis (Q2919690)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Small values of the Euler function and the Riemann hypothesis |
scientific article; zbMATH DE number 6090471
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Small values of the Euler function and the Riemann hypothesis |
scientific article; zbMATH DE number 6090471 |
Statements
Small values of the Euler function and the Riemann hypothesis (English)
0 references
5 October 2012
0 references
Euler's function
0 references
Riemann hypothesis
0 references
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.
0 references
