Loading...
Please wait, while we are loading the content...
Similar Documents
Unimodular roots of special littlewood polynomials.
| Content Provider | CiteSeerX |
|---|---|
| Author | Mercer, Idris David |
| Abstract | Abstract. We call α(z) = a0 + a1z + · · · + an−1zn−1 a Littlewood polynomial if a j = ±1 for all j. We call α(z) self-reciprocal if α(z) = zn−1α(1/z), and call α(z) skewsymmetric if n = 2m + 1 and am+ j = (−1) jam − j for all j. It has been observed that Littlewood polynomials with particularly high minimum modulus on the unit circle in C tend to be skewsymmetric. In this paper, we prove that a skewsymmetric Littlewood polynomial cannot have any zeros on the unit circle, as well as providing a new proof of the known result that a self-reciprocal Littlewood polynomial must have a zero on the unit circle. 1 Introduction and Statement of Results We let Ln denote the set of all 2 n polynomials of the form α(z) = a0 + a1z + · · · + an−1zn−1, where a j = ±1 for all j, and we call such a polynomial a Littlewood polynomial. Erdős, Littlewood, and others |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Unit Circle Special Littlewood Polynomial Littlewood Polynomial Unimodular Root Skewsymmetric Littlewood Polynomial Cannot High Minimum Modulus New Proof Self-reciprocal Littlewood Polynomial |
| Content Type | Text |
| Resource Type | Article |
