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 language | English |
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Pages (from-to) | 181-210 |
Journal | The Ramanujan Journal |
Volume | 221 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2010 |
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)