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On the group extension of the transformation associated to non-archimedean continued fractions

Author: Natsui Rie  

Publisher: Springer Publishing Company

ISSN: 0236-5294

Source: Acta Mathematica Hungarica, Vol.108, Iss.4, 2005-08, pp. : 299-318

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Abstract

Let Fq be a finite field with q elements. We consider formal Laurent series of Fq -coefficients with their continued fraction expansions by Fq -polynomials. We prove some arithmetic properties for almost every formal Laurent series with respect to the Haar measure. We construct a group extension of the non-archimedean continued fraction transformation and show its ergodicity. Then we get some results as an application of the individual ergodic theorem. We also discuss the convergence rate for limit behaviors.