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

abstract

  • We examine the size of a real trigonometric polynomial of degree at most n having at least zeros in K := (mod 27) (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.

published proceedings

  • PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

author list (cited authors)

  • Borwein, P., & Erdelyi, T.

citation count

  • 4

complete list of authors

  • Borwein, P||Erdelyi, T

publication date

  • November 2001