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arXiv · 2107.12510

Higher-rank pointwise discrepancy bounds and logarithm laws for generic lattices

Seungki Kim·Mishel Skenderi
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Abstract

We prove a higher-rank analogue of a well-known result of W. M. Schmidt concerning almost everywhere pointwise discrepancy bounds for lattices in Euclidean space (see Theorem 1 [Trans. Amer. Math. Soc. 95 (1960), 516-529]). We also establish volume estimates pertaining to higher minima of lattices and then use the work of Kleinbock-Margulis and Kelmer-Yu to prove dynamical Borel-Cantelli lemmata and logarithm laws for higher minima and various related functions.

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Seungki Kim, Mishel Skenderi. 2021-07-26. Higher-rank pointwise discrepancy bounds and logarithm laws for generic lattices. https://arxiv.org/abs/2107.12510

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