In this article, we prove the following conjecture by Lubotzky. Let , where is a local field of characteristic and where is a simply connected, absolutely almost simple -group of -rank at least 2. We give the rate of growth of
where if and only if there is an abstract automorphism of such that . We also study the rate of subgroup growth of any lattice in . As a result, we show that these two functions have the same rate of growth, which proves Lubotzky’s conjecture. Along the way, we also study the rate of growth of the number of equivalence classes of maximal lattices in with covolume at most .
"Counting lattices in simple Lie groups: The positive characteristic case." Duke Math. J. 161 (3) 431 - 481, February 2012. https://doi.org/10.1215/00127094-1507421