Applied Physics and Mathematics Annotation << Back ESTIMATE OF THE ASYMPTOTIC BEHAVIOR OF THE MOMENTS OF ARITHMETIC FUNCTIONS HAVING LIMITING NORMAL DISTRIBUTION V.L. VOLFSON Recently, with the development of computer technology and the Internet, the problem of the distribution of prime numbers has acquired important 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 consider a method for estimating the asymptotics of arithmetic functions in the natural series in the paper. This question is closely related to the distribution of primes in natural numbers. Even with the definition of the asymptotics of the mean value of arithmetic functions, problems often arise, and even more so in the determination of the asymptotics of the moments of higher orders. Therefore, the paper proposes a probabilistic approach, different from the traditional one, based on the limiting distribution of arithmetic functions. Arithmetic functions with limiting normal distribution are considered. Several assertions are proved about the estimation of the asymptotics of the moments of strongly additive arithmetic functions, as well as additive functions of the class H and arithmetic functions of the class V having such a limit distribution. Keywords: arithmetic function, additive arithmetic function, strongly additive arithmetic function, probability space, analogue of the law of large numbers, limit distribution, normal distribution, asymptotics of moments of arithmetic functions, sequence of random variables, independence of random variables, Central limit theorem. DOI: 10.25791/pfim.03.2021.1201 Pp. 40-49.