On the Hausdorff dimension of certain sets arising in Number Theory
Abstract
This paper has been withdrawn Any real number x in the unit interval can be expressed as a continued fraction x=[n1,...,n_N,...]. Subsets of zero measure are obtained by imposing simple conditions on the n_N. By imposing n_N m ∀ N∈ , Jarnik defined the corresponding sets Em and gave a first estimate of dH(Em), dH the Hausdorff dimension. Subsequent authors improved these estimates. In this paper we deal with dH(Em) and dH(Fm), Fm being the set of real numbers for which Σi=1N ni N m.
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