English

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 L1L_1 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.

Keywords

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"

R2 v1 2026-06-21T22:03:23.112Z