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Conjugate Reciprocal Polynomials with All Roots on the Unit Circle

Published online by Cambridge University Press:  20 November 2018

Kathleen L. Petersen  and
Christopher D. Sinclair
Kathleen L. Petersen
Affiliation:
Queen’s University, Kingston, ON, K7l 3N5 e-mail:petersen@mast.queensu.ca
Christopher D. Sinclair
Affiliation:
Pacific Institute for the Mathematical Sciences, Vancouver, BC, V6T 1Z4 e-mail:christopher.sinclair@colorado.edu
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Abstract

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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 ${{\mathbb{R}}^{N-1}}$. 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 $2N$.

Keywords

11C0828A7515A5254H1058D19
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 5 , October 2008 , pp. 1149 - 1167
Copyright
Copyright © Canadian Mathematical Society 2008

References

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