Applied Physics and Mathematics Annotation << Back CHARACTERISTICS OF THE SUM OF RANDOM VARIABLES TAKING THE VALUES OF ARITHMETIC FUNCTIONS WITH BOUNDED TERMS V.L. VOLFSON Recently, with the development of computer technology and the Internet, the problem of the distribution of primes has gained important practical importance, since it is directly related to the reliability of the so-called cryptographic systems with a public key. For example, the cryptographic strength of the currently widely used RSA encryption system is based on the computational complexity of factorization of large natural numbers. In this paper, we study the adder arithmetic functions associated with the distribution of primes. The paper gives estimates of the variance of the sum of random variables taking the values of bounded arithmetic functions, as well as some adder arithmetic functions with bounded terms. The statement on this topic is proved and examples are considered. Keywords: summation arithmetic function, bounded arithmetic function, sequence of random variables, Mertens function, Liouville function, Moebius function, number of natural numbers other than squares, limit distribution, normal distribution law, mathematical expectation, variance of the sum of random variables. DOI: 10.25791/pfim.05.2019.924 Contacts: - Pp. 32-35.