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A Gauss–Kuz’min–Lévy theorem for Rényi-type continued fractions

Volume 193 / 2020

Dan Lascu, Gabriela Ileana Sebe Acta Arithmetica 193 (2020), 283-292 MSC: Primary 11J70; Secondary 60A10. DOI: 10.4064/aa181009-18-2 Published online: 27 January 2020

Abstract

We consider an interval map which is a generalization of the Rényi transformation. For the continued fraction expansion arising from this transformation, we prove a result concerning the asymptotic behavior of the distribution functions of this map. More exactly, we use Szüsz’s method to prove a Gauss–Kuz’min–Lévy-type theorem.

Authors

  • Dan LascuMircea cel Batran Naval Academy
    1 Fulgerului
    900218 Constanţa, Romania
    e-mail
  • Gabriela Ileana SebeFaculty of Applied Sciences
    Politehnica University of Bucharest
    Splaiul Independentei 313
    060042 Bucureşti, Romania
    and
    Institute of Mathematical Statistics
    and Applied Mathematics
    Calea 13 Sept. 13
    050711 Bucureşti, Romania
    e-mail

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