Asymptotic normality of b-additive functions on polynomial sequences in number systems

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Abstract

We consider b-additive functions f where b is an algebraic integer over ℤ. In particular, let p be a polynomial, then we show that the asymptotic distribution of f(⌊ p(z)⌋), where ⌊⋅⌋ denotes the integer part with respect to basis b, when z runs through the elements of the ring ℤ[b] is the normal law. This is a generalization of results of Bassily and Kátai (for the integer case) and of Gittenberger and Thuswaldner (for the Gaussian integers).
Original languageEnglish
Pages (from-to)181-210
JournalThe Ramanujan Journal
Volume221
Issue number2
DOIs
Publication statusPublished - 2010

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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