Applied Physics and Mathematics Annotation << Back SUMMATION ARITHMETIC FUNCTIONS WITH BOUNDED TERMS, HAVING A LIMIT NORMAL DISTRIBUTION LAW V.L. VOLFSON Recently, with the development of computer technology and the Internet, the problem of the distribution of primes has acquired important practical significance, since it is directly related to the reliability of the so-called public-key cryptographic systems. For example, the cryptographic strength of the currently widely used RSA encryption system is based on the computational complexity of decomposing into prime factors of large natural numbers. In this paper, we investigate adder arithmetic functions associated with the distribution of prime numbers. The paper considers the properties of pseudo stationarity in a broad sense and pseudo strong mixing for sequences of random variables corresponding to arithmetic functions. Assertions on this topic have been proven. The implementation of these properties for known arithmetic functions has been verified. The article proves a statement about sufficient conditions under which a summation arithmetic function with bounded terms has a limit normal distribution law. The fulfillment of the specified sufficient conditions for known arithmetic functions is considered. Keywords: summation arithmetic function, pairwise asymptotically independent terms, sequence of random variables, pseudo stationarity in the broad sense, pseudo strong mixing, Mertens function, Liouville function, Mobius function, number of natural numbers other than squares, limit distribution, normal distribution law. DOI: 10.25791/pfim.03.2019.726 Contacts: E-mail: znakvicvolf@mail.ru Pp. 58-64.