Abstract
Let $\Omega(n)$ denote the number of prime factors of $n$. We show that for any bounded $f\colon\mathbb{N}\to\mathbb{C}$ one has \[ \frac{1}{N}\sum_{n=1}^N\, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N\, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1). \] This yields a new elementary proof of the Prime Number Theorem.
Details
Title
A new elementary proof of the Prime Number Theorem
Author(s)
Richter, Florian Karl
Published in
Bulletin of the London Mathematical Society
Volume
53
Issue
5
Pages
1365-1375
Date
2021-10
ISSN
0024-6093
1469-2120
1469-2120
Other identifier(s)
View record in ArXiv
Laboratories
ERG
Record Appears in
Scientific production and competences > SB - School of Basic Sciences > MATH - Institute of Mathematics > ERG - Chair of Ergodic Theory
Peer-reviewed publications
Work outside EPFL
Journal Articles
Published
Peer-reviewed publications
Work outside EPFL
Journal Articles
Published
Record creation date
2021-11-26