Mertens和Liouville求和函数的研究
Investigations of Mertens and Liouville summation functions
摘要：
本文研究了Mertens和Liouville的求和算术函数。证明了这些函数的极限分布是正态分布。它还表明，这些函数的标准差的估计$O(n^{1/2})$不能得到改善。得到了Liouville和函数的平均值的估计，以及Mertens和Liouville和函数之比的增长阶的估计.
英文摘要：
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 $O(n^{1/2})$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
