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Applied Physics and Mathematics Annotation << Back
ESTIMATE OF ASYMPTOTICS OF THE MOMENTS OF ARITHMETIC FUNCTIONS HAVING A LIMITING DISTRIBUTION |
V.L. VOLFSON
Recently, with the development of computer technology and the Internet, the problem of the distribution of prime numbers has acquired 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 consider a method for estimating asymptotics of arithmetic functions in the natural series in this paper. This question is closely related to the distribution of prime numbers in natural numbers. Even problems often arise with the definition of asymptotics of the mean value of arithmetic functions, and even more so in the determination of asymptotics of the moments of higher orders. Therefore, the paper proposes a different from the traditional, probabilistic approach based on the limiting distribution of arithmetic functions. We will consider the general case of a method for estimating asymptotics of the moments of additive arithmetic functions having a limit distribution in the paper. Several assertions are proved about the estimation of asymptotics of the moments of strongly additive arithmetic functions, as well as additive functions of the class H having a limit distribution.
Keywords: arithmetic function, additive arithmetic function, strongly additive arithmetic function, probability space, analogue of the law of large numbers, limit distribution, asymptotics of the moments of arithmetic functions, sequence of random variables, independence of random variables, central moment of the k-th order.
DOI: 10.25791/pfim.04.2021.1204
Pp. 17-27. |
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