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

Junda Pan

Let $\mu (n)$ denote the Möbius function, define $M(x)={\sum }_{n\le x}^{}\mu (n)$. The main result of this paper is to prove that \begin{equation*} \displaystyle\lim_{x \to +\infty}\frac…