A Gauss-Kuzmin Theorem for Some Continued Fraction Expansions

Dan Lascu; Katsunori Kawamura

A Gauss-Kuzmin Theorem for Some Continued Fraction Expansions

Number Theory 2013-08-22 v2

Authors: Dan Lascu , Katsunori Kawamura

Abstract

We consider a family of continued fraction expansions of any number in the unit closed interval $[0,1]$ whose digits are differences of consecutive non-positive integer powers of an integer $m \geq 2$ . For this expansion, we apply the method of Rockett and Sz\"usz from [6] and obtained the solution of its Gauss-Kuzmin type problem.

Keywords

Gauss-Kuzmin theorem continued fraction expansions non-positive integer powers unit closed interval

Cite

@article{arxiv.1108.4624,
  title  = {A Gauss-Kuzmin Theorem for Some Continued Fraction Expansions},
  author = {Dan Lascu and Katsunori Kawamura},
  journal= {arXiv preprint arXiv:1108.4624},
  year   = {2013}
}

Comments

This paper has been withdrawn by the author due to the change of the authors team

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