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Horospheres and Farey fractions

Published 24 Mar 2010 in math.DS and math.NT | (1003.4613v2)

Abstract: 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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