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Subgroup growth of lattices in semisimple Lie groups

Abstract:

We give very precise bounds for the congruence subgroup growth of arithmetic groups. This allows us to determine the subgroup growth of irreducible lattices of semisimple Lie groups. In the most general case our results depend on the Generalized Riemann Hypothesis for number fields but we can state the following unconditional theorem: Let $G$ be a simple Lie group of real rank at least 2, different than $D_4(\bbc)$, and let $\Gamma$ be any non-uniform lattice of $G$. Let $s_n(\Gamma)$ denot...

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Publication status:
Published

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Publisher copy:
10.1007/BF02392552

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Journal:
ACTA MATHEMATICA
Volume:
193
Issue:
1
Pages:
105-139
Publication date:
2004-06-09
DOI:
EISSN:
1871-2509
ISSN:
0001-5962
URN:
uuid:2de851bf-1205-4345-a6a0-a9925106598a
Source identifiers:
354356
Local pid:
pubs:354356
Language:
English
Keywords:

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