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Mathematics > Number Theory
Title: Higher-rank pointwise discrepancy bounds and logarithm laws for generic lattices
(Submitted on 26 Jul 2021 (v1), last revised 8 Jul 2022 (this version, v2))
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.
Submission history
From: Mishel Skenderi [view email][v1] Mon, 26 Jul 2021 23:02:39 GMT (19kb)
[v2] Fri, 8 Jul 2022 20:28:28 GMT (23kb)
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