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Bilyk: Roth's orthogonal function method in discrepancy theory
equation_1_14: The counting discrepancy of every planar N-point set has L1 norm at least an absolute constant times the square root of log N.
Dmitriy Bilyk, On Roth's orthogonal function method in discrepancy theory, Uniform Distribution Theory 6 (2011), no. 1, 143--184. The edition read is the 42-page author-hosted journal PDF, listed in the journal issue.
Read status. Claims checked: definition (1.4), p. 145, and Halász's bound (1.14), p. 148. The proof outline (4.15)--(4.17), p. 169, was read from the page image; its earlier Haar estimates and higher-order remainder bound have not been checked. This is Bilyk's exposition of Halász's theorem, not an examination of the original 1981 paper.
The extracted planar L1 bound supplies a precise source interface for Problem 1221.
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