Information Technologies in Computer and Analytical Methods for Modeling the Processes of Forming Classes of Prime Numbers and Estimating the Constants of Artin's Generalized Hypothesis

Abstract

The relationship between the processes of forming classes of prime numbers in the generalized Artin hypothesis is investigated on the basis of the theory of randomization of algorithms of the probabilistic method and analytical number theory. It is proved that probabilistic methods are the basis for constructing computer models for the formation of classes of prime numbers in accordance with Artin's generalized hypothesis. It was found that modern methods of analytical number theory do not allow one to obtain estimates for the generalized Artin constants. Methods for calculating the Artin constants are developed and the convergence of the estimates of the constants in probability to the limiting values is established. The fundamentals of the number-theoretic analysis of Artin's constants and related classes have been created.