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On the distribution for sums of partial quotients in continued fraction expansions
| Content Provider | Scilit |
|---|---|
| Author | Wu, Jun Xu, Jian |
| Copyright Year | 2011 |
| Description | Journal: Nonlinearity Let x [0, 1) and $[a_{1}$(x), $a_{2}$(x), ...] be the continued fraction expansion of x. For any n ≥ 1, write . Khintchine (1935 Compos. Math. 1 361–82) proved that converges in measure to with respect to , where denotes the one dimensional Lebesgue measure. Philipp (1988 Monatsh. Math. 105 195–206) showed that there is not a reasonable normalizing sequence such that a strong law of large numbers is satisfied. In this paper, we show that for any α ≥ 0, the set is of Hausdorff dimension 1. Furthermore, we prove that the Hausdorff dimension of the set consisting of reals whose sums of partial quotients grow at a given polynomial rate is 1. |
| Related Links | http://iopscience.iop.org/article/10.1088/0951-7715/24/4/009/pdf |
| Ending Page | 1187 |
| Page Count | 11 |
| Starting Page | 1177 |
| ISSN | 09517715 |
| e-ISSN | 13616544 |
| DOI | 10.1088/0951-7715/24/4/009 |
| Journal | Nonlinearity |
| Issue Number | 4 |
| Volume Number | 24 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 2011-03-03 |
| Access Restriction | Open |
| Subject Keyword | Journal: Nonlinearity Applied Mathematics Continued Fraction Partial Quotients Fraction Expansions |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics |
