Abstract
In this paper we prove a renewal-type limit theorem. Given α \in (0,1)\backslash \mathbb {Q} and R>0, let qnR be the first denominator of the convergents of which exceeds R. The main result in the paper is that the ratio qnR/R has a limiting distribution as R tends to infinity. The existence of the limiting distribution uses mixing of a special flow over the natural extension of the Gauss map.
Original language | English (US) |
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Pages (from-to) | 643-655 |
Number of pages | 13 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 28 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2008 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics