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

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McKee J., Smyth C.

Open Mathematics

2013

tom 11

nr 5

882-899

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.

Ograniczanie wyników

1 Open Mathematics

1 McKee J.

1 Smyth C.

1 2013

Wyniki wyszukiwania

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