Lattices of minimum covolume are non-uniform

In this article, we prove that a lattice of minimum covolume in a simple Lie group over a local field of positive characteristic is non-uniform if the Weil’s conjecture on Tamagawa numbers [Wei61] holds. This, in part, answers Lubotzky’s conjecture [Lub91] .

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Veröffentlicht in:	Israel journal of mathematics 2013-08, Vol.196 (1), p.363-373
1. Verfasser:	Golsefidy, Alireza Salehi
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Applications of Mathematics Group Theory and Generalizations Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical
Online-Zugang:	Volltext
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Zusammenfassung:	In this article, we prove that a lattice of minimum covolume in a simple Lie group over a local field of positive characteristic is non-uniform if the Weil’s conjecture on Tamagawa numbers [Wei61] holds. This, in part, answers Lubotzky’s conjecture [Lub91] .
ISSN:	0021-2172 1565-8511
DOI:	10.1007/s11856-012-0167-0