On Arithmetic Lattices in the Plane

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 j-invariant corresponding to similarity classes of planar lattices.

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Cite this paper

@inproceedings{Fukshansky2016OnAL, title={On Arithmetic Lattices in the Plane}, author={Lenny Fukshansky and P. Guerzhoy and Florian Luca}, year={2016} }