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.

AMS Subject Classification: Primary: 37A45; Secondary: 11P99, 11C99.