A new elementary proof of the Prime Number Theorem

Let Ω(n) denote the number of prime factors of n. We show that for any bounded f:N→C one has 1N∑n=1Nf(Ω(n)+1)=1N∑n=1Nf(Ω(n))+oN→∞(1).This yields a new elementary proof of the Prime Number Theorem.

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Veröffentlicht in:	The Bulletin of the London Mathematical Society 2021-10, Vol.53 (5), p.1365-1375
1. Verfasser:	Richter, Florian K.
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Sprache:	eng
Schlagworte:	11A41 (primary) 11N05
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description	Let Ω(n) denote the number of prime factors of n. We show that for any bounded f:N→C one has 1N∑n=1Nf(Ω(n)+1)=1N∑n=1Nf(Ω(n))+oN→∞(1).This yields a new elementary proof of the Prime Number Theorem.
doi_str_mv	10.1112/blms.12503
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title	A new elementary proof of the Prime Number Theorem
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