In this paper we prove a renewal-type limit theorem. Given and R>0, let qnR be the first denominator of the convergents of α 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.
|Translated title of the contribution||Renewal-type Limit Theorem for the Gauss map and continued fractions|
|Pages (from-to)||643 - 655|
|Number of pages||13|
|Journal||Ergodic Theory and Dynamical Systems|
|Volume||28, no 2|
|Publication status||Published - Apr 2008|