Higher-rank pointwise discrepancy bounds and logarithm laws for generic lattices
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DOI10.4064/AA220325-17-8zbMATH Open1506.11099arXiv2107.12510OpenAlexW4296849387MaRDI QIDQ5046061
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Publication date: 27 October 2022
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/2107.12510
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