On arithmetic lattices in the plane

On arithmetic lattices in the plane

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 arithmeti...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2017-04, Vol.145 (4), p.1453-1465
Hauptverfasser: FUKSHANSKY, LENNY, GUERZHOY, PAVEL, LUCA, FLORIAN
Format: Artikel
Sprache:eng
Schlagworte:
A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
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Zusammenfassung: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13374