Polynomial cycles in certain rings of rationals
type: Item
instance of: scholarly article
title: Polynomial cycles in certain rings of rationals
zbMATH Open document ID: 1071.11017
author: Władysław Narkiewicz
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2005-06-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/222674
review text: A finite sequence \((x_0; x_1; \ldots; x_n)\) in an integral domain \(R\) is called a polynomial cycle of length \(n\) if \(x_0; x_1; \ldots; x_{n-1}\) are distinct; \(x_n = x_0\); and there exists a polynomial \(f \in R [X]\) such that \(f(x_i) = x_{i+1}\) for \(i = 0; 1; \ldots; n-1\). For a square-free positive integer \(N\); let \(C(N)\) be the set of all lengths of polynomial cycles in \(\mathbb Z [1/N]\). The author explicitly determines \(C(N)\) if \(N\) is odd; \(N = 2\) or \(N = 2p\) for an odd prime \(p\). The investigations are based on the methods and the general finiteness results derived in [\textit{F. Halter-Koch} and \textit{W. Narkiewicz}, ``Scarcity of finite polynomial orbits'', Publ. Math., Debrecen 56, 405-414 (2000; Zbl 0961.11005)].
reviewed by: Franz Halter-Koch
Mathematics Subject Classification ID: 11C08
Mathematics Subject Classification ID: 11D99
Mathematics Subject Classification ID: 11R09
zbMATH DE Number: 2184598
describes a project that uses: PARI/GP
describes a project that uses: KANT/KASH
MaRDI profile type: Publication
OpenAlex ID: W1991308046
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DOI: 10.5802/JTNB.373
description: scientific article; zbMATH DE number 2184598