Lq Norms of Fekete and Related Polynomials

Zeros of Fekete Polynomials

UPPER BOUNDS FOR THE Lq NORM OF FEKETE POLYNOMIALS ON SUBARCS

where the coefficients are Legendre symbols, is called the p-th Fekete polynomial. In this paper the size of the Fekete polynomials on subarcs is studied. We prove essentially sharp bounds for the average value of |fp(z)| , 0 < q < ∞, on subarcs of the unit circle even in the cases when the subarc is rather small. Our upper bounds are matching with the lower bounds proved in a preceding paper f...

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...

An Extremal Property 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...