On the <i>L</i>_<i>q</i> norm of cyclotomic Littlewood polynomials on the unit circle

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 ( P 2ν ) is a sequence of cyclotomic polynomials P 2ν ∈ 2ν , then for every q &gt; 2 with some a = a ( q ) &gt; 1/2 depending only on q , where The case q = 4 of the above result is due to P. Borwein, Choi and Ferguson. We also prove that if ( P 2ν ) is a sequence of cyclotomic polynomials P 2ν ∈ 2ν , then for every 0 &lt; q &lt; 2 with some 0 &lt; b = b ( q ) &lt; 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.

Locations

• Mathematical Proceedings of the Cambridge Philosophical Society - View
• CiteSeer X (The Pennsylvania State University) - View - PDF