On arithmetic lattices in the plane
Number Theory
2016-07-15 v1
Abstract
We investigate similarity classes of arithmetic lattices in the plane. We introduce a natural height function on the set of such similarity classes, and give asymptotic estimates on the number of all arithmetic similarity classes, semi-stable arithmetic similarity classes, and well-rounded arithmetic similarity classes of bounded height as the bound tends to infinity. We also briefly discuss some properties of the -invariant corresponding to similarity classes of planar lattices.
Cite
@article{arxiv.1607.04044,
title = {On arithmetic lattices in the plane},
author = {Lenny Fukshansky and Pavel Guerzhoy and Florian Luca},
journal= {arXiv preprint arXiv:1607.04044},
year = {2016}
}
Comments
13 pages; to appear in Proc. Amer. Math. Soc