A Gauss-Kuzmin Theorem for Some Continued Fraction Expansions

2011/08/23 by Lascu, Dan, Kawamura, Katsunori
#11J70 #11K50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1108.4624

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 ≥ 2. For this expansion, we apply the method of Rockett and Szüsz from [6] and obtained the solution of its Gauss-Kuzmin type problem.

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