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On the Hausdorff dimension of certain sets arising in Number Theory

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 Added by Eda Cesaratto
 Publication date 1999
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and research's language is English
 Authors Eda Cesaratto




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This paper has been withdrawn Any real number $x$ in the unit interval can be expressed as a continued fraction $x=[n_1,...,n_{_N},...]$. Subsets of zero measure are obtained by imposing simple conditions on the $n_{_N}$. By imposing $n_{_N}le m forall Nin zN$, Jarnik defined the corresponding sets $E_m$ and gave a first estimate of $d_H(E_m)$, $d_H$ the Hausdorff dimension. Subsequent authors improved these estimates. In this paper we deal with $d_H(E_m)$ and $d_H(F_m)$, $F_m$ being the set of real numbers for which ${sum_{i=1}^N n_iover N}le m$.



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245 - Jianing Li 2021
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