Farey Statistics in Time n^{2/3} and Counting Primitive Lattice Points in Polygons
Number Theory
2011-11-10 v2
Abstract
We present algorithms for computing ranks and order statistics in the Farey sequence, taking time O (n^{2/3}). This improves on the recent algorithms of Pawlewicz [European Symp. Alg. 2007], running in time O (n^{3/4}). We also initiate the study of a more general algorithmic problem: counting primitive lattice points in planar shapes.
Keywords
Cite
@article{arxiv.0708.0080,
title = {Farey Statistics in Time n^{2/3} and Counting Primitive Lattice Points in Polygons},
author = {Mihai Patrascu},
journal= {arXiv preprint arXiv:0708.0080},
year = {2011}
}
Comments
Fixed a technical error. Added reference to latest work (joint version with Pawlewicz)