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On an extremal property of the Rudin-Shapiro sequence

Published online by Cambridge University Press:  26 February 2010

Jean-Paul Allouche  and
Michel Mendès France
Jean-Paul Allouche
Affiliation:
U.E.R. de Mathématique, Universté de Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France.
Michel Mendès France
Affiliation:
U.E.R. de Mathématique, Université de Bordeaux I, 351 Cours de La Liberation, 33405 Talence Cedex, France.
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Abstract

Extending the well-known property of the Rudin- Shapiro sequence ε = (ε(n)) with values in {−1, +1} satisfying

we show that for all unimodular 2-multiplicative sequences f = (f(n))

Type
Research Article
Information
Mathematika , Volume 32 , Issue 1 , June 1985 , pp. 33 - 38
Copyright
Copyright © University College London 1985

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References

1.Allouche, J. P. and Mendès France, M.. Suite de Rudin-Shapiro et modèle d'Ising. To appear in Bull. Soc. Math. France, 1985.CrossRefGoogle Scholar
2.Brilhart, J. and Carlitz, L.. Note on the Shapiro polynomials. Proc. Amer. Math. Soc, 25 (1970), 114–119.CrossRefGoogle Scholar
3.Brilhart, J., Erdős, P. and Morton, P.. On sums of Rudin-Shapiro coefficients II. Pac. J. Math, 107 (1983), 39–69.CrossRefGoogle Scholar
4.Christol, G., Kamae, T., Mendès France, M. and Rauzy, G.. Suites algébriques, automates et substitutions. Bull. Soc. Math. France, 108 (1980), 401–419.CrossRefGoogle Scholar
5.Gelfond, A. O.. Sur les nombres qui ont des propriétés additives et multiplicatives données. Acta Arith., 13 (1968), 259–265.CrossRefGoogle Scholar
6.Kahane, J. P. and Salem, R.. Ensemblesparfaits et séries trigonométriques (Hermann, Paris, 1963).Google Scholar
7.Mahler, K.. On the translation properties of a simple class of arithmetical functions. J. Math. and Phys., 6 (1927), 158–163.CrossRefGoogle Scholar
8.Mendès France, M.. Les suites à spectre vide et la répartition modulo 1. J. Number Theory, 5 (1973), 1–15.CrossRefGoogle Scholar
9.Mendés France, M. and Tenenbaum, G.. Dimension des courbes planes, papiers pliés et suite de Rudin-Shapiro. Bull. Soc. Math. France, 109 (1981), 207–215.CrossRefGoogle Scholar
10.Morse, M.. Recurrent geodesies on a surface of negative curvature. Trans. Amer. Math. Soc., 22 (1921), 84–100.CrossRefGoogle Scholar
11.Rudin, W.. Some theorems on Fourier coefficients. Proc. Amer. Math. Soc., 10 (1959), 855–859.CrossRefGoogle Scholar
12.Shapiro, H. S.. Extremal problems for polynomials and power series. Thesis (M.I.T., 1951).Google Scholar
13.Thue, A.. Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Videnskapsselskapets Skrifter, I. Mat. nat. Kl, Kristiania (1906), 1–22.Google Scholar