An Elementary Proof of the Prime Number Theorem based on Möbius Function

2023/02/21 by Junda Pan, Pan, Junda
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2302.12218

openalex publication_date 2023/02/21 · openalex created_date 2023/02/25 · openalex updated_date 2026/07/28

Abstract

Let μ(n) denote the Möbius function, define M(x)= ∑_{n≤ x}μ(n). The main result of this paper is to prove that lim_{x → +∞}(M(x))/(x)=0 which is equivalent to the prime number theorem. We also use Selberg's asymptotic formula, but the treatments of key parts are different from several classical proofs.

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