Armen Vagharshakyan
Published 2012-09-11, updated 2012-11-06Version 2
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.
Comments: a slightly different version of the article is accepted to "Mathematika"
The discrepancy of a needle on a checkerboard, II
Discrete Analogues in Harmonic Analysis: Directional Maximal Functions in $\mathbb{Z}^2$
The discrepancy of a needle on a checkerboard
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