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A logarithm law for automorphism groups of trees

Sa'ar Hersonsky·Frederic Paulin
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Abstract

Let Γbe a geometrically finite tree lattice. We prove a Khintchine-Sullivan type theorem for the Hausdorff measure of the points at infinity of the tree that are well approximated by the parabolic fixed points of G. Using Bruhat-Tits trees, an application is given for the Diophantine approximation of formal Laurent series in the variable 1/X over the finite field Fq by rational fractions in X over Fq, satisfying some congruence properties

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Sa'ar Hersonsky, Frederic Paulin. 2006-12-08. A logarithm law for automorphism groups of trees. https://arxiv.org/abs/math/0511231

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