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- W2009787064 abstract "We give estimates on the number $AL_H(x)$ 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 compute the limit of $log AL_H(x) / xlog x$ when $xtoinfty$. The proofs use several different techniques: geometric (bounding the number of generators of $Gamma$ as a function of its covolume), number theoretic (bounding the number of maximal such $Gamma$) and sharp estimates on the character values of the symmetric groups (to bound the subgroup growth of $Gamma$)." @default.
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- W2009787064 date "2008-11-15" @default.
- W2009787064 modified "2023-09-23" @default.
- W2009787064 title "Counting arithmetic lattices and surfaces" @default.
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