Applied Physics and Mathematics Annotation << Back ESTIMATION OF ASYMPTOTICS OF MOMENTS OF ARITHMETIC FUNCTIONS HAVING A LIMIT DISTRIBUTION IN AN ARITHMETIC PROGRESSION V.L. VOLFSON Recently, with the development of computer technology and the Internet, the problem of the distribution of prime numbers has become of great practical importance, 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 factoring large natural numbers into prime factors. We study asymptotics of t moments of arithmetic functions in an arithmetic progression, which have a limit distribution that is not necessarily normal in this paper. Even with the definition of the asymptotic of the mean value of arithmetic functions, problems often arise, and even more so when determining asymptotics of moments of higher orders. Therefore, the paper proposes a probabilistic approach, different from the traditional one, based on the limiting distribution of arithmetic functions. We consider the general case of the method for estimating asymptotics of moments of additive arithmetic functions on an arithmetic progression that have a limit distribution. Several assertions are proved on estimating asymptotics of moments of strongly additive arithmetic functions, as well as additive functions of the class H, which have a limit distribution on an arithmetic progression. Keywords: arithmetic function, additive arithmetic function, strongly additive arithmetic function, probability space, analogue of the law of large numbers, limit distribution, asymptotics of moments of arithmetic functions on an arithmetic progression, sequence of random variables, independence of random variables, central moment of the k-th order. DOI: 10.25791/pfim.02.2022.1226 Pp. 38-48.