On Arithmetic Lattices in the Plane

Authors

Lenny Fukshansky, Claremont McKenna CollegeFollow
Pavel Guerzhoy, University of Hawaii, Honolulu
Florian Luca, University of Witwatersrand

Document Type

Article - preprint

Publication Date

2016

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.

Comments

Source: Author's pre-print manuscript in PDF.

Rights Information

© 2016 Fukshansky, Guerzhoy, Luca

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

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