Journal of the European Mathematical Society
Full-Text PDF (552 KB) | Metadata | Table of Contents | JEMS summary
Published online: 2009-06-30
On Kahane's ultraflat polynomialsEnrico Bombieri and Jean Bourgain (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