Minimal Mahler measure in real quadratic fields
We consider upper and lower bounds on the minimal height of an irrational number lying in a particular real quadratic field.
math.NT↗
arXiv subjects
Craig Spencer
Publications and source records attributed to Craig Spencer.
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.
math.CA↗