On a discrete approach to lower bounds in discrepancy theory
Classical Analysis and ODEs
2025-03-06 v2 Number Theory
Abstract
In this paper, we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the unit cube due to Roth holds true also for a suitable finite family of corners. We also prove two analogous results for the discrepancy on the torus with respect to squares and balls.
Cite
@article{arxiv.2312.10668,
title = {On a discrete approach to lower bounds in discrepancy theory},
author = {Luca Brandolini and Bianca Gariboldi and Giacomo Gigante and Alessandro Monguzzi},
journal= {arXiv preprint arXiv:2312.10668},
year = {2025}
}
Comments
29 pages, 1 figure. Accepted for publication on Journal of Fourier Analysis and Applications