Integer points on spheres and their orthogonal grids
Number Theory
2017-05-17 v2 Dynamical Systems
Abstract
The set of primitive vectors on large spheres in the euclidean space of dimension d>2 equidistribute when projected on the unit sphere. We consider here a refinement of this problem concerning the direction of the vector together with the shape of the lattice in its orthogonal complement. Using unipotent dynamics we obtained the desired equidistribution result in dimension d>5 and in dimension d=4,5 under a mild congruence condition on the square of the radius. The case of d=3 is considered in a separate paper.
Keywords
Cite
@article{arxiv.1411.1272,
title = {Integer points on spheres and their orthogonal grids},
author = {Menny Aka and Manfred Einsiedler and Uri Shapira},
journal= {arXiv preprint arXiv:1411.1272},
year = {2017}
}
Comments
20 pages. To appear in the Journal of the London Mathematical Society