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arXiv · 1607.04044

On arithmetic lattices in the plane

Lenny Fukshansky·Pavel Guerzhoy·Florian Luca
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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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Lenny Fukshansky, Pavel Guerzhoy, Florian Luca. 2016-07-14. On arithmetic lattices in the plane. https://arxiv.org/abs/1607.04044

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