International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 115-124

On the diaphony of one class of one-dimensional sequences

Vassil St. Grozdanov

Department of Mathematics, University of Blagoevgrad, Blagoevgrad 2700, Bulgaria

Received 7 November 1991; Revised 15 August 1992

Copyright © 1996 Vassil St. Grozdanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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(N1(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(N1(logN)1/2) of the quadratic discrepancy