Horospheres and Farey fractions

Details Horospheres and Farey fractions Horospheres and Farey fractions

2010-03-24

arxiv.org/abs/1003.4613v2

Mathematics

Dynamical Systems

10 pages

Scientific paper

We embed multidimensional Farey fractions in large horospheres and explain
under which conditions they become uniformly distributed in the ambient
homogeneous space. This question has recently been investigated in the case of
SL(d,Z) to prove the asymptotic distribution of Frobenius numbers. The present
paper extends these studies to general lattices in SL(d,R).

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