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1. CMB 2006 (vol 49 pp. 438)
Unimodular Roots of\\ Special Littlewood Polynomials We call $\alpha(z) = a_0 + a_1 z + \dots + a_{n-1} z^{n-1}$ a Littlewood
polynomial if $a_j = \pm 1$ for all $j$. We call $\alpha(z)$ self-reciprocal
if $\alpha(z) = z^{n-1}\alpha(1/z)$, and call $\alpha(z)$ skewsymmetric if
$n = 2m+1$ and $a_{m+j} = (-1)^j a_{m-j}$ for all $j$. It has been observed
that Littlewood polynomials with particularly high minimum modulus on
the unit
circle in $\bC$ 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.
Categories:26C10, 30C15, 42A05 |
2. CMB 2000 (vol 43 pp. 105)
Sets of Uniqueness for Univalent Functions We observe that any set of uniqueness for the Dirichlet space $\cD$
is a set of uniqueness for the class $S$ of normalized univalent
holomorphic functions.
Categories:30C55, 30C15 |