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arXiv · 2101.04931

Counting in generic lattices and higher rank actions

Michael Björklund·Alexander Gorodnik
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Abstract

We consider the problem of counting lattice points contained in domains in $\mathbb{R}^d$ defined by products of linear forms and we show that the normalized discrepancies in these counting problems satisfy non-degenerate Central Limit Theorems, provided that $d \geq 9$. We also study more refined versions pertaining to "spiraling of approximations". Our techniques are dynamical in nature and exploit effective exponential mixing of all orders for actions of higher-rank abelian groups on the space of unimodular lattices.

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Michael Björklund, Alexander Gorodnik. 2021-01-13. Counting in generic lattices and higher rank actions. https://arxiv.org/abs/2101.04931

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