Journal of the European Mathematical Society

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Volume 11, Issue 3, 2009, pp. 627–703
DOI: 10.4171/JEMS/163

Published online: 2009-06-30

On Kahane's ultraflat polynomials

Enrico Bombieri[1] and Jean Bourgain[2]

(1) Institute for Advanced Study, Princeton, United States
(2) Institute for Advanced Study, Princeton, United States

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.

Keywords: Trigonometric polynomials, probabilistic methods, exponential sums

Bombieri Enrico, Bourgain Jean: On Kahane's ultraflat polynomials. J. Eur. Math. Soc. 11 (2009), 627-703. doi: 10.4171/JEMS/163