Article
Sets of Exact Approximation Order by Rational Numbers Ii
Authors
Abstract
For a non-increasing function Ψ, let Exact(Ψ) be the set of real numbers that are approximable by rational numbers to order Ψ, but to no or- der cΨ with 0 < c < 1. In a previous paper, we determined the Hausdorff dimension of the set Exact(Ψ) when x→ x2Ψ(x) is non-increasing and the sumxΨ(x) converges. In the present note we complement this result by estab- x≥1 lishing that Exact(Ψ) has full Hausdorff dimension for a large class of functions Ψthat do not decrease too slowly and are such that the sum xΨ(x) diverges. x≥1 Furthermore, we discuss the case where x→ x2Ψ(x) is a constant function.
Keywords
Diophantine approximation, Hausdorff dimension, continued fraction, Lagrange.
Citation
Bugeaud, Y. (2008). Sets of exact approximation order by rational numbers ii. Uniform Distribution Theory, 3(2), 9–20.
Y. Bugeaud, “Sets of exact approximation order by rational numbers ii,” Uniform Distribution Theory, vol. 3, no. 2, pp. 9–20, 2008.
Bugeaud Y. Sets of exact approximation order by rational numbers ii. Uniform Distribution Theory. 2008;3(2):9–20.
Bugeaud, Y. (2008), ‘Sets of exact approximation order by rational numbers ii’, Uniform Distribution Theory, 3(2), pp. 9–20.
Bugeaud, Yann. “Sets of Exact Approximation Order by Rational Numbers Ii.” Uniform Distribution Theory, vol. 3, no. 2, 2008, pp. 9–20.
Bugeaud, Yann. “Sets of Exact Approximation Order by Rational Numbers Ii.” Uniform Distribution Theory 3, no. 2 (2008): 9–20.
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Published by: Engineering Journals
