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Sur la singularité des produits de Riesz et des mesures spectrales associées à la somme des chiffres

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Abstract

Using a property of generalized characters, we first prove that two Riesz products with constant coefficients and distinct Fourier spectra are mutually singular. IfS r (n) denotes the sum of digits in ther-adic representation of the integern, the same technique allows us to establish the mutual singularity of the spectral measures of the sequences: α(n)=exp[2iπaS p (n)],β(n)=exp[2iπbS q (n)], for every pair of integersp≠q, a, b being real numbers such thata(p−1)∉ {tiZ} andb(q−1)∉Z. This result has been proved by T. Kamae whenp andq are two relatively prime integers.

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  1. U.E.R. de Mathermatique Paris XIII CSP, 93430, Villetaneuse, France

    M. Queffelec

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  1. M. Queffelec
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Queffelec, M. Sur la singularité des produits de Riesz et des mesures spectrales associées à la somme des chiffres. Israel J. Math. 34, 337–342 (1979). https://doi.org/10.1007/BF02760612

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  • DOI: https://doi.org/10.1007/BF02760612

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