Applied Physics and Mathematics Annotation << Back ASYMPTOTIC OF SUMMATION FUNCTIONS V.L. VOLFSON Recently, with the development of computer technology and the Internet, the problem of the distribution of primes has acquired important practical importance, since it is directly related to the reliability of the so-called cryptographic systems with a public key. For example, the cryptographic strength of the currently widely used RSA encryption system is based on the computational complexity of factorization of large natural numbers. In the paper, we will study the asymptotic behavior of summation functions of a natural argument, including the asymptotic behavior of summation functions of a prime argument. Keywords: arithmetic function, summation function, Moebius function, Mertens function, asymptotic upper bound, Macleron’s formula, natural argument, prime argument, prime number. DOI: 10.25791/pfim.03.2020.1164 Pp. 39-42.