Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros

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 pol...

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Bibliographic Details
Published in:Central European journal of mathematics 2013-05, Vol.11 (5), p.882-899
Main Authors: McKee, James, Smyth, Chris
Format: Article
Language:English
Subjects:
11C08
11R06
Algebra
Cyclotomic polynomials
Disc-bionic
Geometry
Interlacing
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Pisot polynomials
Polynomials
Probability Theory and Stochastic Processes
Research Article
Topological Groups
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Summary: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.
ISSN:1895-1074
2391-5455
1644-3616
2391-5455
DOI:10.2478/s11533-013-0209-9