Unimodular roots of reciprocal Littlewood polynomials
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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 Littlewood 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 [수식] for positive integer N > 2 .
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 Littlewood 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 [수식] for positive integer N > 2 .
참고문헌 (19)
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