On the Lq norm of cyclotomic Littlewood polynomials on the unit circle Academic Article uri icon

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) is a sequence of cyclotomic polynomials P, then for every q > 2 with some a = a(q) > 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) is a sequence of cyclotomic polynomials P, then for 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.

author list (cited authors)

  • ERDÉLYI, T.

citation count

  • 1

publication date

  • July 2011