On theLqnorm of cyclotomic Littlewood polynomials on the unit circle

Abstract

Letnbe the collection of all (Littlewood) polynomials of degreenwith coefficients in {−1, 1}. In this paper we prove that if (P2ν) is a sequence of cyclotomic polynomialsP2ν∈2ν, thenfor everyq> 2 with somea=a(q) > 1/2 depending only onq, whereThe caseq= 4 of the above result is due to P. Borwein, Choi and Ferguson. We also prove that if (P2ν) is a sequence of cyclotomic polynomialsP2ν∈2ν, thenfor every 0 <q< 2 with some 0 <b=b(q) < 1/2 depending only onq. Similar results are conjectured for Littlewood polynomials of odd degree. Our main tool here is the Borwein–Choi Factorization Theorem.