A Gauss-Kuzmin Theorem for Some Continued Fraction Expansions

Details A Gauss-Kuzmin Theorem for Some Continued Fraction Expansions A Gauss-Kuzmin Theorem for Some Continued Fraction Expansions

2011-08-23

arxiv.org/abs/1108.4624v1

Mathematics

Number Theory

7 pages

Scientific paper

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.

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