TY - JOUR

T1 - Conjugate reciprocal polynomials with all roots on the unit circle

AU - Petersen, Kathleen L.

AU - Sinclair, Christopher D.

PY - 2008/10

Y1 - 2008/10

N2 - 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.

AB - 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.

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U2 - 10.4153/CJM-2008-050-8

DO - 10.4153/CJM-2008-050-8

M3 - Article

AN - SCOPUS:53549127851

VL - 60

SP - 1149

EP - 1167

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

SN - 0008-414X

IS - 5

ER -