Length of the powers of a rational fraction
type: Item
instance of: scholarly article
title: Length of the powers of a rational fraction
zbMATH Open document ID: 0878.11028
author: Guillaume Grisel
published in: Journal of Number Theory
publication date: 1998-01-12T00:00:00Z
review text: Let \(k\) be a field and let \(\alpha\) be a rational fraction of \(k(x)\) whose continued fraction expansion is \([a_0,a_1,\dots, a_s]\), with length \(D(\alpha)= s+1\). In the paper under review, the author shows that \(D(\alpha^n)\) tends to infinity with \(n\) provided the characteristic of \(k\) is 0, \(\alpha\) is not a polynomial nor the reciprocal of a polynomial. The author also deals with the case of non-zero characteristic.
Mathematics Subject Classification ID: 11J70
Mathematics Subject Classification ID: 11A55
zbMATH DE Number: 992064
zbMATH Keywords: function fields
zbMATH Keywords: rational fraction
zbMATH Keywords: continued fraction expansion
zbMATH Keywords: length
reviewed by: Claude Levesque
MaRDI profile type: Publication
full work available at URL: jnth.1997.2054
OpenAlex ID: W2078464384
cites work: Q3885825
cites work: Q4124903
cites work: Q4156489
cites work: Q4405256
cites work: Sur les fractions continues limitées
cites work: Q3331273
DOI: 10.1006/JNTH.1997.2054
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description: scientific article; zbMATH DE number 992064