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