Publication

A new elementary proof of the Prime Number Theorem

Florian Karl Richter
2021
Journal paper

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.

Official source

https://infoscience.epfl.ch/record/290218?ln=en

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