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On the Lq norm of cyclotomic Littlewood polynomials on the unit circle

Published online by Cambridge University Press:  13 July 2011

TAMÁS ERDÉLYI
TAMÁS ERDÉLYI*
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843, U.S.A. e-mail: terdelyi@math.tamu.edu
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Abstract

Let n be the collection of all (Littlewood) polynomials of degree n with coefficients in {−1, 1}. In this paper we prove that if (P2ν) is a sequence of cyclotomic polynomials P2ν ∈ 2ν, thenfor every q > 2 with some a = a(q) > 1/2 depending only on q, whereThe case q = 4 of the above result is due to P. Borwein, Choi and Ferguson. We also prove that if (P2ν) is a sequence of cyclotomic polynomials P2ν ∈ 2ν, thenfor every 0 < q < 2 with some 0 < b = b(q) < 1/2 depending only on q. Similar results are conjectured for Littlewood polynomials of odd degree. Our main tool here is the Borwein–Choi Factorization Theorem.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 2 , September 2011 , pp. 373 - 384
Copyright
Copyright © Cambridge Philosophical Society 2011

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References

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