A new elementary proof of the Prime Number Theorem

DOI10.1112/BLMS.12503zbMATH Open1485.11139arXiv2002.03255OpenAlexW3005523650MaRDI QIDQ5021652

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Publication date: 13 January 2022

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Abstract: Let $Omega(n)$ denote the number of prime factors of $n$. We show that for any bounded $fcolonmathbbNomathbbC$ 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 oinfty}(1). ] This yields a new elementary proof of the Prime Number Theorem.

Full work available at URL: https://arxiv.org/abs/2002.03255

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