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.
|Titolo:||On the rational approximations to the powers of an algebraic number: solution of two problems of Mahler and Mendès France|
|Data di pubblicazione:||2004|
|Parole Chiave:||Diophantine Approximation; Continued fractions|
|Appare nelle tipologie:||1.1 Articolo in rivista|