Abstract
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.
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McKee, J., Smyth, C. Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros. centr.eur.j.math. 11, 882–899 (2013). https://doi.org/10.2478/s11533-013-0209-9
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DOI: https://doi.org/10.2478/s11533-013-0209-9