Characteristic polynomial patterns in difference sets of matrices. (16th February 2016) - Björklund, Michael; Fish, Alexander
Abstract : We show that for every subsetE of positive density in the set of integer square‐matrices with zero traces, there exists an integerk ⩾ 1 such that the set of characteristic polynomials of matrices inE - E contains the set of all characteristic polynomials of integer matrices with zero traces and entries divisible byk . Our theorem is derived from results by Benoist–Quint on measure rigidity for actions on homogeneous spaces.