Characteristic Polynomial Patterns in Difference Sets of Matrices
Björklund, Michael · Fish, Alexander
Original · EN
We show that for every subset E of positive density in the set of integer square-matrices with zero traces, there exists an integer k ≥ 1 such that the set of characteristic polynomials of matrices in E-E contains the set of all characteristic polynomials of integer matrices with zero traces and entries divisible by k. Our theorem is derived from results by Benoist-Quint on measure rigidity for actions on homogeneous spaces.
English translation
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