## On Bohr sets of integer-valued traceless matrices

### Alexander Fish

#### 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 of Burgain–Furman–Lindenstrauss–Mozes.

Keywords: Ergodic Ramsey Theory, Measure Rigidity, Analytic Number Theory.

: Primary: 37A45; Secondary: 11P99, 11C99.

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 Tuesday, December 8, 2015