The limiting distribution function for the Mobius function is found in the paper. It is proved also the relation: $\lim_{n \to \infty} {P(S_n/\sqrt {2pn}<y)}=G(y)$, where $S_n$ is the sum of random variables having the distribution of the Mobius function, $G(y)$ is a function of the standard normal distribution and $p=3/\pi^2$. It is shown that the law of the iterated logarithm is fulfilled for the sum of random variables having the distribution of the Mobius function. 查看全文>>