Investigations of Mertens and Liouville summation functions

Summation arithmetic functions of Mertens and Liouville are investigated in the paper. It is proved that the limiting distribution of these functions is the normal. It is also shown that the estimating of standard deviation of these functions $O(n^{1\mathrm{/}2})$ cannot be improved. The estimate of the average of Liouville summation function is found. The estimate of the order of growth of the ratio of the summation functions of Mertens and Liouville is also found.