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. 627–703DOI 10.4171/JEMS/163