Determination of the asymptotic behavior of probabilistic characteristics of arithmetic functions and some other questions of probabilistic number theory

2020/12/03 by Victor Volfson, Volfson, Victor
Mathematics · #Probability and Statistical Research #advanced mathematical theories #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2012.08934

Abstract

One of the questions of distribution of prime numbers is considered in the article. It is shown what error is obtained from the assumption that the asymptotic density of a sequence of primes is a probability. Various forms of an analogue of the law of large numbers for arithmetic functions and, in particular, the Hardy-Ramunajan theorem are obtained. A method is given for finding asymptotics of the probabilistic characteristics of arithmetic functions.

Related

• Probabilistic analytical approach to determining the asymptotics of prime objects on the initial interval of the natural series
• Asymptotics of probability characteristics of additive arithmetic functions
• Probabilistic approach to the distribution of primes and to the proof of Legendre and Elliott-Halberstam conjectures
• The distribution of prime numbers and tuples in the natural numbers
• On limiting distributions of arithmetic functions