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.References
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Additional Information
- Lenny Fukshansky
- Affiliation: Department of Mathematics, Claremont McKenna College, 850 Columbia Avenue, Claremont, California 91711
- MR Author ID: 740792
- Email: lenny@cmc.edu
- Pavel Guerzhoy
- Affiliation: Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, Hawaii 96822-2273
- Email: pavel@math.hawaii.edu
- Florian Luca
- Affiliation: School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Johannesburg, South Africa – and – Centro de Ciencias Matemáticas, UNAM, Morelia, México
- MR Author ID: 630217
- Email: Florian.Luca@wits.ac.za
- Received by editor(s): November 18, 2015
- Received by editor(s) in revised form: June 9, 2016
- Published electronically: October 18, 2016
- Additional Notes: The first author was partially supported by the NSA grant H98230-1510051
The second author was partially supported by a Simons Foundation Collaboration Grant - Communicated by: Matthew A. Papanikolas
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1453-1465
- MSC (2010): Primary 11H06, 11G50, 11A25, 11G05
- DOI: https://doi.org/10.1090/proc/13374
- MathSciNet review: 3601538