Lower Bounds for $L_1$ Discrepancy

Abstract

We find the best asymptotic lower bounds for the coefficient of the leading term of the $L_1$ 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.

a slightly different version of the article is accepted to "Mathematika"

References in corpus (1)

• On lower bounds for the L_2-discrepancy