JournalsjemsVol. 11, No. 3pp. 627–703

On Kahane's ultraflat polynomials

  • Jean Bourgain

    Institute for Advanced Study, Princeton, United States
  • Enrico Bombieri

    Institute for Advanced Study, Princeton, United States
On Kahane's ultraflat polynomials cover

Abstract

This paper is devoted to the construction of polynomials of almost constant modulus on the unit circle, with coefficients of constant absolute value. In particular, one obtains a much improved estimate for the error term. A major part of this paper deals also with the long-standing problem of the effective construction of ultraflat polynomials.

Cite this article

Jean Bourgain, Enrico Bombieri, On Kahane's ultraflat polynomials. J. Eur. Math. Soc. 11 (2009), no. 3, pp. 627–703

DOI 10.4171/JEMS/163