Trigonometric polynomials with many real zeros and a Littlewood-type problem Academic Article uri icon


  • We examine the size of a real trigonometric polynomial of degree at most n having at least κ zeros in K := ℝ (mod 27π) (counting multiplicities). This result is then used to give a new proof of a theorem of Littlewood concerning flatness of unimodular trigonometric polynomials. Our proof is shorter and simpler than Littlewood's. Moreover our constant is explicit in contrast to Littlewood's approach, which is indirect. © 2000 Copyright retained by the authors.

author list (cited authors)

  • Borwein, P., & Erdélyi, T.

citation count

  • 3

publication date

  • November 2000