Acta Mathematica Hungarica
Volume/Issue:
Volume 108: Issue 4
On the group extension of the transformation associated to non-archimedean continued fractions
Author:
Rie Natsui Department of Mathematics, Keio University 3-14-1 Hiyoshi, Kohoku-Ku, Yokohama, 223-8522 Japan

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Pages:
299–318
Online Publication Date:
08 Sep 2005
Publication Date:
01 Aug 2005
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-005-0226-7
Keywords:
Non-archimedean continued fractions; metric theory; ergodic group extension
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Summary 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.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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