MODELING THE PROCESSES OF FORMING CLASSES OF PRIME NUMBERS AND EVALUATING THE CONSTANTS OF ARTIN’S GENERALIZED HYPOTHESIS ON THE BASIS OF ANALYTICAL AND COMPUTER METHODS OF THEIR FORMATION

 

1. Vostrov, R. Opiata

Odessa national polytechnic university

 

Abstract. The analysis of the relationship between the processes of forming classes of prime numbers in the generalized hypothesis of Artin is carried out on the basis of the theory of randomization of algorithms of the probabilistic method and analytical number theory. Probabilistic methods of constructing computer models for the formation of classes of prime numbers in accordance with Artin’s generalized hypothesis are investigated. It is proved that modern methods of analytical number theory do not allow obtaining estimates for generalized Artin constants. A method for calculating Artin’s constants is developed and the convergence of the estimates of the constants in probability to the limiting values is established. The basic principles of the number-theoretic analysis of Artin’s constants and related classes are formulated.

Key word: generalized Artin classes, Artin’s constants, class probabilities, stability of estimates for Artin’s constants, convergence in probability.