TY - JOUR
T1 - Counting non-uniform lattices
AU - Belolipetsky, Mikhail
AU - Lubotzky, Alexander
N1 - Publisher Copyright:
© 2019, The Hebrew University of Jerusalem.
PY - 2019/8/1
Y1 - 2019/8/1
N2 - 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(γ(H)+o(1)) log x/ log log x where γ(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.
AB - 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(γ(H)+o(1)) log x/ log log x where γ(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.
UR - http://www.scopus.com/inward/record.url?scp=85070382240&partnerID=8YFLogxK
U2 - 10.1007/s11856-019-1868-4
DO - 10.1007/s11856-019-1868-4
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AN - SCOPUS:85070382240
SN - 0021-2172
VL - 232
SP - 201
EP - 229
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -