Counting integral matrices with a given characteristic polynomial
Representation Theory
2011-11-10 v1 Number Theory
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.
Cite
@article{arxiv.math/0002179,
title = {Counting integral matrices with a given characteristic polynomial},
author = {Nimish A. Shah},
journal= {arXiv preprint arXiv:math/0002179},
year = {2011}
}