Integer points and their orthogonal lattices
Number Theory
2016-12-21 v1 Dynamical Systems
Abstract
Linnik proved in the late 1950's the equidistribution of integer points on large spheres under a congruence condition. The congruence condition was lifted in 1988 by Duke (building on a break-through by Iwaniec) using completely different techniques. We conjecture that this equidistribution result also extends to the pairs consisting of a vector on the sphere and the shape of the lattice in its orthogonal complement. We use a joining result for higher rank diagonalizable actions to obtain this conjecture under an additional congruence condition.
Cite
@article{arxiv.1502.04209,
title = {Integer points and their orthogonal lattices},
author = {Menny Aka and Manfred Einsiedler and Uri Shapira},
journal= {arXiv preprint arXiv:1502.04209},
year = {2016}
}
Comments
15 pages, and 6 pages of appendix, (Appendix by Ruixiang Zhang)