Lower Bounds for $L_1$ Discrepancy
Classical Analysis and ODEs
2022-11-29 v2 Number Theory
Probability
Abstract
We find the best asymptotic lower bounds for the coefficient of the leading term of the norm of the two-dimensional (axis-parallel) discrepancy that can be obtained by K.Roth's orthogonal function method among a large class of test functions. We use methods of combinatorics, probability, complex and harmonic analysis.
Cite
@article{arxiv.1209.2398,
title = {Lower Bounds for $L_1$ Discrepancy},
author = {Armen Vagharshakyan},
journal= {arXiv preprint arXiv:1209.2398},
year = {2022}
}
Comments
a slightly different version of the article is accepted to "Mathematika"