Loading...
Please wait, while we are loading the content...
Similar Documents
Unimodular Roots of Special Littlewood Polynomials
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mercer, Idris David |
| Copyright Year | 2006 |
| Abstract | We call �(z) = a0 + a1z + � � � + an 1z n 1 a Littlewood polynomial if a j = ±1 for all j. We call �(z) self-reciprocal if �(z) = z n 1 �(1/z), and call �(z) skewsymmetric if n = 2m + 1 and am+ j = (−1) j am 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. |
| Starting Page | 438 |
| Ending Page | 447 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| DOI | 10.4153/cmb-2006-043-x |
| Volume Number | 49 |
| Alternate Webpage(s) | http://idmercer.com/mercer8549.pdf |
| Alternate Webpage(s) | https://doi.org/10.4153/cmb-2006-043-x |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
