Counting arithmetic lattices and surfaces

• 成果类型: Article
• 署名作者: Belolipetsky, Mikhail; Gelander, Tsachik; Lubotzky, Alexander; Shalev, Aner
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.172.2197
• 发表日期: 2010
• 页码: 2197-2221
• 关键词: subgroup growth; MANIFOLDS

摘要

We give estimates on the number AL(H)(x) of conjugacy classes of arithmetic lattices Gamma of covolume at most x in a simple Lie group H. In particular, we obtain a first concrete estimate on the number of arithmetic 3-manifolds of volume at most x. Our main result is for the classical case H = PSL(2, R) where we show that