Conjugate reciprocal polynomials with all roots on the unit circle

Kathleen L. Petersen, Christopher D. Sinclair

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We study the geometry, topology and Lebesgue measure of the set of monk 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 ℝN-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.

Original languageEnglish (US)
Pages (from-to)1149-1167
Number of pages19
JournalCanadian Journal of Mathematics
Issue number5
StatePublished - Oct 2008
Externally publishedYes


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