Geodesic
Counting arithmetic subgroups and subgroup growth of virtually free groups
Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 925-953

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DOI

Let K be a p-adic field, and let H=PSL2​(K) endowed with the Haar measure determined by giving a maximal compact subgroup measure 1. Let ALH​(x) denote the number of conjugacy classes of arithmetic lattices in H with co-volume bounded by x. We show that under the assumption that K does not contain the element ζ+ζ−1, where ζ denotes the p-th root of unity over Qp​, we have
DOI : 10.4171/jems/522
Classification : 22-XX, 20-XX
Keywords: Arithmetic subgroups, counting lattices, subgroup growth, virtually free groups 
Amichai Eisenmann. Counting arithmetic subgroups and subgroup growth of virtually free groups. Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 925-953. doi: 10.4171/jems/522
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     author = {Amichai Eisenmann},
     title = {Counting arithmetic subgroups and subgroup growth of virtually free groups},
     journal = {Journal of the European Mathematical Society},
     pages = {925--953},
     year = {2015},
     volume = {17},
     number = {4},
     doi = {10.4171/jems/522},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/522/}
}
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