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research article
A new elementary proof of the Prime Number Theorem
October 2021
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.
Type
research article
ArXiv ID
2002.03255
Authors
Publication date
2021-10
Published in
Volume
53
Issue
5
Start page
1365
End page
1375
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
November 26, 2021
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