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arXiv:1305.5563 [math.NT]AbstractReferencesReviewsResources

A gauss-kuzmin theorem and related questions for $θ$-expansions

Gabriela Ileana Sebe, Dan Lascu

Published 2013-05-23Version 1

Using the natural extension for $\theta$-expansions, we give an infinite-order-chain representation of the sequence of the incomplete quotients of these expansions. Together with the ergodic behavior of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.

Comments: 27 pages
Categories: math.NT, math.DS
Subjects: 11A55, 11K50
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