In this paper we present some results related to the problem of finding periodic representations for algebraic numbers. In particular, we analyze the problem for cubic irrationalities. We show an interesting relationship between the convergents of bifurcating continued fractions related to a couple of cubic irrationalities, and a particular generalization of the R´edei polynomials. Moreover, we give a method to construct a periodic bifurcating continued fraction for any cubic root paired with another determined cubic root
Titolo: | PERIODIC REPRESENTATIONS FOR CUBIC IRRATIONALITIES | |
Autori Riconosciuti: | ||
Autori: | MARCO ABRATE; STEFANO BARBERO; UMBERTO CERRUTI; NADIR MURRU | |
Data di pubblicazione: | 2012 | |
Abstract: | In this paper we present some results related to the problem of finding periodic representations for algebraic numbers. In particular, we analyze the problem for cubic irrationalities. We show an interesting relationship between the convergents of bifurcating continued fractions related to a couple of cubic irrationalities, and a particular generalization of the R´edei polynomials. Moreover, we give a method to construct a periodic bifurcating continued fraction for any cubic root paired with another determined cubic root | |
Volume: | 50 | |
Pagina iniziale: | 252 | |
Pagina finale: | 264 | |
URL: | http://arxiv.org/pdf/1304.2906.pdf | |
Rivista: | THE FIBONACCI QUARTERLY | |
Appare nelle tipologie: | 03A-Articolo su Rivista |
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File | Descrizione | Tipologia | Licenza | |
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Periodic Representations for Cubic Irrationalities.pdf | POSTPRINT (VERSIONE FINALE DELL’AUTORE) | Accesso aperto | Open Access Visualizza/Apri |
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