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Applied Physics and Mathematics

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ASYMPTOTICS OF PROBABILITY CHARACTERISTICS OF ADDITIVE ARITHMETIC FUNCTIONS
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 study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the estimation of the asymptotics of the probabilistic characteristics of strongly additive arithmetic functions, as well as additive functions of the class that have the same asymptotic behavior of the probabilistic characteristics, as for strongly additive arithmetic functions.
Keywords: arithmetic function, additive arithmetic function, strongly additive arithmetic function, asymptotics of probabilistic characteristics of arithmetic functions.


DOI: 10.25791/pfim.05.2021.1210

Pp. 36-41.

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