Exponents of Diophantine approximation and expansions in integer bases
- Autores: Masaaki Amou, Yann Bugeaud
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 2, 2010, págs. 297-316
- Idioma: inglés
- DOI: 10.1112/jlms/jdp070
- Enlaces
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Resumen
Let î be a real number and let b 2 be an integer. Let vb(î) or v b(î) denote the supremum of the real numbers v for which the equation bnî (bn) .v or br(bs . 1)î (br+s) .v has infinitely many solutions in positive integers n or r and s, respectively. Here, · stands for the distance to the nearest integer. Also let v1(î) denote the supremum of the real numbers v for which the equation qî < q .v has infinitely many solutions in positive integers q. Motivated by the question whether one can read the irrationality exponent of a real number on its b-ary expansion, we establish various results on the set of values taken by the triple of functions (v1, vb, v b) evaluated at real points.
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