Counting non-uniform lattices

被引：1
|
作者：
Belolipetsky, Mikhail [1 ]
Lubotzky, Alexander [2 ]
机构：
[1] Inst Nacl Matemat Pura & Aplicada, Estr Dona Castorina 100, BR-22460320 Rio De Janeiro, Brazil
[2] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2019年 / 232卷 / 01期
基金：
欧洲研究理事会;
关键词：
ALGEBRAIC-GROUPS; SUBGROUP GROWTH; NUMBER; EXISTENCE;
D O I：
10.1007/s11856-019-1868-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In [BGLM] and [GLNP] it was conjectured that if H is a simple Lie group of real rank at least 2, then the number of conjugacy classes of (arithmetic) lattices in H of covolume at most x is x((gamma(H)+o(1)) log x/ log log x) where gamma(H) is an explicit constant computable from the (absolute) root system of H. In [BLu] we disproved this conjecture. In this paper we prove that for most groups H the conjecture is actually true if we restrict to counting only non-uniform lattices.
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页码：201 / 229
页数：29
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