Estimates of nonuniformity of distributions of congruent sums of random variables (Q1377931)

The aim of the paper is to present a further development of the well-known fact that congruent summation of independent random variables modulo 1 increases the degree of a distribution uniformity. The authors analyze the degree of uniformity of the distribution for a determinate sequence of numbers from \((0, 1)\) that are obtained by the congruent summation of weakly bounded original sequences, provide a theoretical basis for improving the quality of pseudo-random numbers by congruent summation, and show that a special attention has to be paid to the independence of sequences (i.e. to the possibility of factorization of joint frequencies) coming into the congruent summation.