| Title: |
A unifying theory for metrical results on regular continued fraction convergents and mediants |
| Authors: |
DAJANI, KARMA; KRAAIKAMP, COR; SANDERSON, SLADE; Mathematical Modeling; Sub Mathematical Modeling |
| Publication Year: |
2025 |
| Subject Terms: |
Taverne; Algebra and Number Theory; Computational Mathematics; Applied Mathematics |
| Description: |
We revisit Ito’s [Osaka J. Math. 26 (1989), pp. 557–578] natural extension of the Farey tent map, which generates all regular continued fraction convergents and mediants of a given irrational. With a slight shift in perspective on the order in which these convergents and mediants arise, this natural extension is shown to provide an elegant and powerful tool in the metric theory of continued fractions. A wealth of old and new results—including limiting distributions of approximation coefficients, analogues of a theorem of Legendre and their refinements, and a generalisation of L´evy’s Theorem to subsequences of convergents and mediants—are presented as corollaries within this unifying theory. |
| Document Type: |
article in journal/newspaper |
| File Description: |
application/pdf |
| Language: |
English |
| ISSN: |
0025-5718 |
| Relation: |
https://dspace.library.uu.nl/handle/1874/478647 |
| Availability: |
https://dspace.library.uu.nl/handle/1874/478647 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.B058B488 |
| Database: |
BASE |