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http://dx.doi.org/10.4134/JKMS.2008.45.3.835

UNIMODULAR ROOTS OF RECIPROCAL LITTLEWOOD POLYNOMIALS  

Drungilas, Paulius (Department of Mathematics and Informatics Vilnius University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.3, 2008 , pp. 835-840 More about this Journal
Abstract
The main result of this paper shows that every reciprocal Littlewood polynomial, one with {-1, 1} coefficients, of odd degree at least 7 has at least five unimodular roots, and every reciprocal Little-wood polynomial of even degree at least 14 has at least four unimodular roots, thus improving the result of Mukunda. We also give a sketch of alternative proof of the well-known theorem characterizing Pisot numbers whose minimal polynomials are in $$A_N=\{[{X^d+ \sum\limits^{d-1}_{k=0} a_k\;X^k{\in} \mathbb{Z}[X]\;:\;a_k={\pm}N,\;0{\leqslant}k{\leqslant}d-1}\}$$ for positive integer $N{\geqslant}2$.
Keywords
Pisot numbers; Littlewood polynomials; unimodular roots; reciprocal polynomiab;
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