Fekete-like polynomials

Zeros of Fekete Polynomials

Some Numerical Results on Fekete Polynomials

It is known that if x is a real residue character modulo k with x(p) = — 1 k n for the first five primes p, then the corresponding Fekete polynomial £„=j X(n)x changes sign on (0, 1). In this paper it is shown that the condition that x(p) be — 1 for the first four primes p is not sufficient to guarantee such a sign change. More specifically, if x ¡s the real nonprincipal character modulo either...

An Extremal Property of Fekete Polynomials

Fekete Polynomials and Shapes of Julia Sets

We prove that a nonempty, proper subset S of the complex plane can be approximated in a strong sense by polynomial filled Julia sets if and only if S is bounded and Ĉ \ int(S) is connected. The proof that such a set is approximable by filled Julia sets is constructive and relies on Fekete polynomials. Illustrative examples are presented. We also prove an estimate for the rate of approximation i...

Fekete Points

In this communication we present a new method to estimate Fekete points on surfaces. Our method works in a general setting, in the sense that we can obtain good estimations of the Fekete points on piecewise regular surfaces. The determination of Fekete points in the unit sphere is considered as a model of a highly non-linear optimization problem with non-linear constraints. In fact, obtaining a...