Abstract
In Sections 4 through 11 of this paper we study the phase behaviour, on the unit circle, for the so called “ultraflat unimodular polynomials” the existence of which is known since Kahane’s celebrated 1980 paper [7]. Before doing so we recall, in Sections 2 and 3, some definitions and historical background.
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Bibliography
N.K. Bari (Bary). A treatise on trigonometric series, volume II. Pergamon,New York, 1964.
J. Beck. “flat” polynomials on the unit circle-on a problem of Little-wood.To appear.
S.N. Bernstein. Sur la convergence absolute des séries trigonométriques. C.R. Acad. Sci. Paris, pages 1661–1663,1914.
J.S. Byrnes. On polynomials with coefficients of modulus one. Bull. London Math. Soc., 9:171–176,1977.
P. Erdös. Some unsolved problems. Michigan Mathematical Journal 4:291–300,1957.
M.L. Fredman, B. Saffari, and B. Smith. Polynômes réciproques. C.R. Acad. Sci. Paris, 308:461–464,1989.
J.-P Kahane. Sur les polynômes à coefficients unimodulaires. Bull. London Math. Soc., 12:321–342,1980.
T. Körner. On a polynomial of J.S. Byrnes. Bull. London Math. Soc., 12:219–224,1980.
J.E. Littlewood. On polynomials ∑±zm/ ∑ exp(αmi)zm, z = eøi. Journal London Math. Soc., 41:367–376,1966.
J.E. Littlewood. Some problems in real and complex analysis. Heath, 1968.
H. Queffelec and B. Saffari. On Kahane’s ultraflat polynomials. Preprint.
B. Saffari. Cross-means and functions of mean value zero. In Proc. of Symposium in honour of H. Delange, Orsay, 1982.
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© 1992 Springer Science+Business Media Dordrecht
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Saffari, B. (1992). The phase behaviour of ultraflat unimodular polynomials. In: Byrnes, J.S., Byrnes, J.L., Hargreaves, K.A., Berry, K. (eds) Probabilistic and Stochastic Methods in Analysis, with Applications. NATO ASI Series, vol 372. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2791-2_26
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DOI: https://doi.org/10.1007/978-94-011-2791-2_26
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