Geodesic
On Kahane's ultraflat polynomials
Journal of the European Mathematical Society, Tome 11 (2009) no. 3, pp. 627-703
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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.
DOI : 10.4171/jems/163
Classification : 12-XX, 11-XX, 00-XX
Keywords: Trigonometric polynomials, probabilistic methods, exponential sums 
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     author = {Enrico Bombieri and Jean Bourgain},
     title = {On {Kahane's} ultraflat polynomials},
     journal = {Journal of the European Mathematical Society},
     pages = {627--703},
     year = {2009},
     volume = {11},
     number = {3},
     doi = {10.4171/jems/163},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/163/}
}
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Enrico Bombieri; Jean Bourgain. On Kahane's ultraflat polynomials. Journal of the European Mathematical Society, Tome 11 (2009) no. 3, pp. 627-703. doi: 10.4171/jems/163

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