Discrepancies and their means
Classical Analysis and ODEs
2023-09-06 v1 Combinatorics
Abstract
It is shown that the discrepancy function for point distributions on a torus is expressed by an explicit formula in terms of its mean values on sub-tori. As an application of this formula, a simple proof of a theorem of Lev on the equivalence of - and shifted -discrepancies is given.
Cite
@article{arxiv.2309.01547,
title = {Discrepancies and their means},
author = {M. M. Skriganov},
journal= {arXiv preprint arXiv:2309.01547},
year = {2023}
}