On the Real Part of Ultraflat Sequences of Unimodular Polynomials
نویسنده
چکیده
Let Pn(z) = ∑n k=0 ak,nz k ∈ C[z] be a sequence of unimodular polynomials (|ak,n| = 1 for all k, n) which is ultraflat in the sense of Kahane, i.e., lim n→∞ max |z|=1 ∣
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How Far Is an Ultraflat Sequence of Unimodular Polynomials from Being Conjugate-reciprocal?
In this paper we study ultraflat sequences (Pn) of unimodular polynomials Pn ∈ Kn in general, not necessarily those produced by Kahane in his paper [Ka]. We examine how far is a sequence (Pn) of unimodular polynomials Pn ∈ Kn from being conjugate reciprocal. Our main results include the following. Theorem. Given a sequence (εn) of positive numbers tending to 0, assume that (Pn) is a (εn)-ultraf...
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