Higher-rank pointwise discrepancy bounds and logarithm laws for generic lattices
Number Theory
2022-07-12 v2 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2107.12510,
title = {Higher-rank pointwise discrepancy bounds and logarithm laws for generic lattices},
author = {Seungki Kim and Mishel Skenderi},
journal= {arXiv preprint arXiv:2107.12510},
year = {2022}
}
Comments
Made some corrections and changes following a referee report