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

DOI: https://doi.org/10.15276/eltecs.34.110.2021.8
Keywords: generalized Artin classes, Artin’s constants, class probabilities, stability of estimates for Artin’s constants, convergence in probability.

Abstract

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.

Author Biographies

George Vostrov, Odessa Polytechnic State University

 Ph. D. of Technical Sciences, Associate Professor of the Department of Applied Mathematics and Information Technologies

Roman Opiata, Odessa Polytechnic State University

PhD student of the Department of Applied Mathematics and Information Technologies

Published
2021-09-03
Issue
No. 34(110) (2021): Electrotechnic and computer system
Section
Computer Systems, Networks and their Components