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A new elementary proof of the Prime Number Theorem (2002.03255v3)

Published 9 Feb 2020 in math.NT

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.

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