Directional discrepancy in two dimensions

In the present paper, we study the geometric discrepancy with respect to families of rotated rectangles. The well‐known extremal cases are the axis‐parallel rectangles (logarithmic discrepancy) and rectangles rotated in all possible directions (polynomial discrepancy). We study several intermediate situations: lacunary sequences of directions, lacunary sets of finite order, and sets with small Minkowski dimension. In each of these cases, extensions of a lemma due to Davenport allow us to construct appropriate rotations of the integer lattice which yield small discrepancy.

• Publication year

  2009

• Venue

  Bulletin of the London Mathematical Society

• Publication date

  2009-11-20

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1112/blms/bdr050arXiv 0911.3971
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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