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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


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.


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

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