Asymptotic normality of \(b\)-additive functions on polynomial sequences in the Gaussian number field
type: Item
instance of: scholarly article
title: Asymptotic normality of \(b\)-additive functions on polynomial sequences in the Gaussian number field
zbMATH Open document ID: 0989.11040
author: Bernhard Gittenberger
author: Jörg M. Thuswaldner
published in: Journal of Number Theory
publication date: 2001-01-01T00:00:00Z
review text: The authors consider the asymptotic behaviour of \(b\)-additive functions \(f\) with respect to a base \(b\) of a canonical number system in the Gaussian number field. In particular, a normal limit law for \(f (P(z))\) is proved, where \(P(z)\) is a polynomial with integer coefficients. The proofs depend on methods from the theory of exponential sums and on results from the theory of uniform distribution.
Mathematics Subject Classification ID: 11K65
Mathematics Subject Classification ID: 11A63
zbMATH DE Number: 1547367
zbMATH Keywords: canonical number systems
zbMATH Keywords: distribution problems
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: normal limit law
reviewed by: Robert F. Tichy
MaRDI profile type: Publication
full work available at URL: jnth.2000.2522
OpenAlex ID: W2035527090
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DOI: 10.1006/JNTH.2000.2522
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description: scientific article; zbMATH DE number 1547367