On arithmetic lattices in the plane

Fukshansky, Lenny; Guerzhoy, Pavel; Luca, Florian

doi:10.1090/proc/13374

On arithmetic lattices in the plane
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by Lenny Fukshansky, Pavel Guerzhoy and Florian Luca PDF

Proc. Amer. Math. Soc. 145 (2017), 1453-1465 Request permission

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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