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Journal Articles Acta Arithmetica Year : 2008

Block additive functions on the Gaussian integers

Abstract

We present three conceptually different methods to prove distribution results for block additive functions with respect to radix expansions of the Gaussian integers. Based on generating function approaches we obtain a central limit theorem and asymptotic expansions for the moments. Furthermore, these generating functions as well as ergodic skew products are used to prove uniform distribution in residue classes and modulo 1.
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Dates and versions

hal-00871045 , version 1 (31-10-2013)

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Michael M. Drmota, Peter Grabner, Pierre Liardet. Block additive functions on the Gaussian integers. Acta Arithmetica, 2008, 135 (4), pp.299--332. ⟨10.4064/aa135-4-1⟩. ⟨hal-00871045⟩
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