UNIMODULAR ROOTS OF RECIPROCAL LITTLEWOOD POLYNOMIALS

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 i