Article - preprint
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.
© 2016 Fukshansky, Guerzhoy, Luca
Fukshansky, L., Guerzhoy, P., Luca, F., On arithmetic lattices in the plane, to appear in the Proceedings of the American Mathematical Society.