Applied Physics and Mathematics Annotation << Back SUMMATION ARITHMETIC FUNCTIONS WITH ASYMPTOTICALLY INDEPENDENT SUMMANDS 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. The summation arithmetic functions with asymptotically independent terms in this paper are studied. We prove assertions about the condition under which the summation arithmetic functions have asymptotically independent summands. It is also proved that under certain conditions on summands of the summation arithmetic function, the limiting distribution of the summation arithmetic function is normal. Keywords: summation function, asymptotically independent summands, Mertens function, Liouville function, Mobius function, number of square-free numbers, limiting distribution of summation functions, normal distribution. DOI: 10.25791/pfim.06.2018.332 Contacts: E-mail: znakvicvolf@mail.ru Pp. 40-47.