On Bohr sets of integer-valued traceless matrices
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.
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