The paper completely solves two questions of K. Mahler and resp. M. Mendes-France, on the rational approximations to the powers of an algebraic numbers (and the continued fractions for these powers). The methods are new and rely on the Subspace Theorem. An Appendix shows that in a sense some of the results are best-possible.

On the rational approximations to the powers of an algebraic number: solution of two problems of Mahler and Mendès France

ZANNIER, UMBERTO;
2004

Abstract

The paper completely solves two questions of K. Mahler and resp. M. Mendes-France, on the rational approximations to the powers of an algebraic numbers (and the continued fractions for these powers). The methods are new and rely on the Subspace Theorem. An Appendix shows that in a sense some of the results are best-possible.
Diophantine Approximation; Continued fractions
File in questo prodotto:
File Dimensione Formato  
Acta Math.2004.Corvaja.pdf

Accesso chiuso

Tipologia: Altro materiale allegato
Licenza: Non pubblico
Dimensione 769.96 kB
Formato Adobe PDF
769.96 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/6538
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 17
social impact