The discrepancy of C-uniformly distributed multidimensional functions

Irregularities of continuous distributions

“…The lower bound (7) of Theorem 1 is due to R. J. Taschner [10] (see also [5]). where * denotes the convolution operation.…”

“…By using p = pn and q = pn^-i {pn is the n-th prime number satisfying pn ~ n \ogn) we can deduce (10) (132) ^\s) < Q + 0(1)) s-2 \s -oo) .…”

“…Such a function can be interpreted as a particle's movement on 'R, K /Z K . It is of some interest to consider a measure for the irregularity of the distribution behaviour of this particle, the discrepancy i and the volume of R. R. J. Taschner [10] was the first who noticed that the discrepancy cannot be too small. He proved that for K > 2 (…”