Lower bounds for the directional discrepancy with respect to an interval of rotations

2022/09/24 by Dmitriy Bilyk, Bilyk, Dmitriy, Michelle Mastrianni +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2209.12098

openalex publication_date 2022/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the lower bound for the optimal directional discrepancy with respect to the class of rectangles in ℝ² rotated in a restricted interval of directions [-θ, θ] with θ< \fracπ4 is of the order at least N^1/5 with a constant depending on θ.

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