On the height of cyclotomic polynomials
Bartłomiej Bzdęga (2012)
Acta Arithmetica
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Bartłomiej Bzdęga (2012)
Acta Arithmetica
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Andrej Dujella, Tomislav Pejković (2011)
Rendiconti del Seminario Matematico della Università di Padova
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I. R. Shafarevich (1999)
The Teaching of Mathematics
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H. Kaufman, Mira Bhargava (1965)
Collectanea Mathematica
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Wolfgang Schmidt (1977)
Acta Arithmetica
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Miloš Kössler (1951)
Czechoslovak Mathematical Journal
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Christoph Schwarzweller, Artur Korniłowicz (2016)
Formalized Mathematics
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In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.
Toufik Zaïmi (2011)
Publications de l'Institut Mathématique
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James McKee, Chris Smyth (2013)
Open Mathematics
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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,...