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Counting integral matrices with a given characteristic polynomial

Nimish A. Shah
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Abstract

We give a simpler proof of an earlier result giving an asymptotic estimate for the number of integral matrices, in large balls, with a given monic integral irreducible polynomial as their common characteristic polynomial. The proof uses equidistributions of polynomial trajectories on SL(n,R)/SL(n,Z), which is a generalization of Ratner's theorem on equidistributions of unipotent trajectories. We also compute the exact constants appearing in the above mentioned asymptotic estimate.

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Nimish A. Shah. 2000-02-22. Counting integral matrices with a given characteristic polynomial. https://arxiv.org/abs/math/0002179

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