Applied Physics and Mathematics Annotation << Back INVESTIGATION OF THE MITTENS AND LIOUVILLE SUMMATION FUNCTIONS V.L. VOLFSON Recently, with the development of computer technology and the Internet, the problem of the distribution of prime numbers has acquired an important practical significance, since it is directly related to the reliability of so-called cryptographic systems with a public key. For example, the cryptographic resistance of the widely used RSA encryption system is based on the computational complexity of prime factorization of large natural numbers. In this paper we investigate the arithmetic functions associated with the distribution of prime numbers. 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(n1/2) cannot be improved. The estimate of the average of the Liouville summation function is found. The estimate of the order of growth of the ratio of the summation functions of Mertens and Liouville is found. Keywords: summation function, Mertens function, Liouville function, Miebius function, Liouville arithmetic function, limit distribution of summation functions, normal distribution, standard deviation, estimation of the order of growth of Mittens and Liouville summation functions. DOI: 10.25791/pfim.04.2018.145 Contacts: E-mail: znakvicvolf@mail.ru Pp. 52-58.