On the Hausdorff dimension of certain sets arising in Number Theory

1999/08/10 by Eda Cesaratto, Cesaratto, Eda
Mathematics · #11K55 #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math/9908043

openalex publication_date 1999/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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This paper has been withdrawn Any real number x in the unit interval can be expressed as a continued fraction x=[n₁,...,n_N,...].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∈ \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 ∑_i=1^N n_i\over N≤ m.

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