二维方向差异
Directional discrepancy in two dimensions
摘要：
本文研究了旋转矩形族的几何不一致性。著名的极端情况是轴平行的矩形（对数差异）和矩形旋转在所有可能的方向（多项式差异）。我们研究了几种中间情况：方向的缺项序列，有穷级的缺项集和Minkowski维数小的集。在每一种情况下，由于达文波特引理的扩展，使我们能够构建适当的旋转的整数格产生小的差异。
英文摘要：
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.
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