Conjugate Reciprocal Polynomials with all Roots on the Unit Circle

Details Conjugate Reciprocal Polynomials with all Roots on the Unit Circle Conjugate Reciprocal Polynomials with all Roots on the Unit Circle

2005-11-15

arxiv.org/abs/math/0511397v1

Mathematics

Number Theory

18 pages, 3 figures

Scientific paper

We study the geometry, topology and Lebesgue measure of the set of monic conjugate reciprocal polynomials of fixed degree with all roots on the unit circle. The set of such polynomials of degree N is naturally associated to a subset of $\R^{N-1}$. We calculate the volume of this set, prove the set is homeomorphic to the $N-1$ ball and that its isometry group is isomorphic to the dihedral group of order $2N$.

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