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

• Autorzy: James McKee , Chris Smyth
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Cyclotomic polynomials; Interlacing; Pisot polynomials; Disc-bionic

Kategorie tematyczne

• 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure
• 11C08: Polynomials

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 5
• Strony: 882-899

Daty

wydano

2013-05-01

online

2013-03-14

Twórcy

autor

James McKee

• University of London

autor

Chris Smyth

• University of Edinburgh, Edinburgh

Bibliografia

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• [11] McKee J., Smyth C.J., There are Salem numbers of every trace, Bull. London Math. Soc., 2005, 37(1), 25–36 http://dx.doi.org/10.1112/S0024609304003790
• [12] McKee J., Smyth C.J., Salem numbers, Pisot numbers, Mahler measure and graphs, Experiment. Math., 2005, 14(2), 211–229 http://dx.doi.org/10.1080/10586458.2005.10128915
• [13] McKee J., Smyth C.J., Salem numbers and Pisot numbers via interlacing, Canad. J. Math., 2012, 64(2), 345–367 http://dx.doi.org/10.4153/CJM-2011-051-2
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Identyfikatory

DOI

10.2478/s11533-013-0209-9