On dispersion and Markov constants

Abstract

We proved some results on the dispersion of the real quadratic irrational numbers, and use LEO 386/25 to compute some numerical results when the dsicriminant d < 200. The details are as follows. Let {xn} be a sequence of numbers, 0 ≤ xn ≤ 1. H. Niederreiter introduced a measure of denseness of such a sequence as follows. For each N, let (Formula Presented.) and define (Formula Presented.). In particular, for irrational α, the dispersion constant D(α) is defined by D({nα mod 1}).