Intersecting lines modulo one

Huxley, Martin Neil 2013. Intersecting lines modulo one. Uniform Distribution Theory 8 (2) , pp. 1-28.

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Abstract

A straight line in the plane of gradient α reduces modulo the integer lattice to a set of parallel lines across the unit square. When α is irrational, these lines are dense in the unit square. Two straight lines with different irrational gradients α and β give two dense families of parallel lines, whose intersections are uniformly distributed in the unit square. The discrepancy bounds involve continued fractions, or linear forms in α and β.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Mathematical Institute of the Slovak Academy of Sciences
ISSN:	1336-913X
Last Modified:	04 Jun 2017 06:19
URI:	https://orca.cardiff.ac.uk/id/eprint/58598

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