On Bohr sets of integer-valued traceless matrices
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Abstract:
In this paper we show that any Bohr-zero non-periodic set $B$ of traceless integer-valued matrices, denoted by $\Lambda$, intersects non-trivially the conjugacy class of any matrix from $\Lambda$. As a corollary, we obtain that the family of characteristic polynomials of $B$ contains all characteristic polynomials of matrices from $\Lambda$. The main ingredient used in this paper is an equidistribution result for an $SL_d(\mathbb {Z})$ random walk on a finite-dimensional torus deduced from Bourgain-Furman-Lindenstrauss-Mozes work [J. Amer. Math. Soc. 24 (2011), 231–280].References
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Additional Information
- Alexander Fish
- Affiliation: School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006 Australia
- MR Author ID: 774403
- Email: alexander.fish@sydney.edu.au
- Received by editor(s): June 7, 2016
- Received by editor(s) in revised form: June 20, 2016, and March 21, 2017
- Published electronically: August 30, 2017
- Communicated by: Nimish Shah
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 625-636
- MSC (2010): Primary 37A45; Secondary 11P99, 11C99
- DOI: https://doi.org/10.1090/proc/13743
- MathSciNet review: 3731697