We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class, the cyclogenic Pisot polynomials. We investigate properties of this class of Pisot polynomials.
@article{bwmeta1.element.doi-10_2478_s11533-013-0209-9,
author = {James McKee and Chris Smyth},
title = {Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {882-899},
zbl = {1272.11113},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0209-9}
}
James McKee; Chris Smyth. Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros. Open Mathematics, Tome 11 (2013) pp. 882-899. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0209-9/
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