Distribution of the values ofq-additive functions on polynomial sequences

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1995 English Publisher:Springer Science and Business Media LLCJournal:Acta Mathematica Hungarica, volume 68, pages 353-361 (issn: 0236-5294, eissn: 1588-2632,

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Authors: Bassily, N. L.; Kátai, I.;

doi: 10.1007/bf01874349

Distribution of the values ofq-additive functions on polynomial sequences

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Abstract

Let \(f\) be a \(q\)-additive function and \(P\) a polynomial with integer coefficients. The authors show that under some conditions the frequencies of \(f\circ P\) converge to the normal distribution function. They use theorems of Vinogradov and Hua for trigonometric sums and of Erdös and Turán for the discrepancy of sequences mod 1.

Related Organizations

Ain Shams University
Egypt

Keywords

Distribution functions associated with additive and positive multiplicative functions, normal distribution function, Arithmetic functions in probabilistic number theory, \(q\)-additive function, frequencies

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