International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 115-124
doi:10.1155/S016117129600018X

On the diaphony of one class of one-dimensional sequences

Abstract

In the present paper, we consider a problem of distribution of sequences in the interval [0,1), the so-called 'Pr-sequences' We obtain the best possible order O(N−1(logN)1/2) for the diaphony of such Pr-sequences. For the symmetric sequences obtained by symmetrization of Pr-sequences, we get also the best possible order O(N−1(logN)1/2) of the quadratic discrepancy