Geodesic
Conjugate Reciprocal Polynomials with All Roots on the Unit Circle
Canadian journal of mathematics, Tome 60 (2008) no. 5, pp. 1149-1167

Voir la notice de l'article provenant de la source Cambridge University Press

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 $2N$ .
DOI : 10.4153/CJM-2008-050-8
Mots-clés : 11C08, 28A75, 15A52, 54H10, 58D19 
Petersen, Kathleen L.; Sinclair, Christopher D. Conjugate Reciprocal Polynomials with All Roots on the Unit Circle. Canadian journal of mathematics, Tome 60 (2008) no. 5, pp. 1149-1167. doi: 10.4153/CJM-2008-050-8
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