# American Institute of Mathematical Sciences

2017, 24: 110-122. doi: 10.3934/era.2017.24.012

## Central limit theorems in the geometry of numbers

 1 Department of Mathematics, Chalmers, Gothenburg, Sweden 2 University of Bristol, Bristol, UK

Received  June 28, 2017 Published  October 2017

We investigate in this paper the distribution of the discrepancy of various lattice counting functions. In particular, we prove that the number of lattice points contained in certain domains defined by products of linear forms satisfies a Central Limit Theorem. Furthermore, we show that the Central Limit Theorem holds for the number of rational approximants for weighted Diophantine approximation in $\mathbb{R}^d$. Our arguments exploit chaotic properties of the Cartan flow on the space of lattices.

Citation: Michael Björklund, Alexander Gorodnik. Central limit theorems in the geometry of numbers. Electronic Research Announcements, 2017, 24: 110-122. doi: 10.3934/era.2017.24.012
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