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arXiv · 1209.2398

Lower Bounds for $L_1$ Discrepancy

Armen Vagharshakyan
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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.

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BibTeXRIS

Armen Vagharshakyan. 2012-09-11. Lower Bounds for $L_1$ Discrepancy. https://doi.org/10.1112/s0025579312001180

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