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arXiv · 1207.0954

Fine-scale statistics for the multidimensional Farey sequence

Jens Marklof
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Abstract

We generalize classical results on the gap distribution (and other fine-scale statistics) for the one-dimensional Farey sequence to arbitrary dimension. This is achieved by exploiting the equidistribution of horospheres in the space of lattices, and the equidistribution of Farey points in a certain subspace of the space of lattices. The argument follows closely the general approach developed by A. Str\"ombergsson and the author [Annals of Math. 172 (2010) 1949--2033].

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Jens Marklof. 2012-07-04. Fine-scale statistics for the multidimensional Farey sequence. https://arxiv.org/abs/1207.0954

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