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The theta group and the continued fraction expansion with even partial quotients
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kraaikamp, Cornelis Lopes, Artur O. |
| Copyright Year | 1996 |
| Abstract | F. Schweiger introduced the continued fraction with even partial quotients. We will show a relation between closed geodesics for the theta group (the subgroup of the modular group generated by z+2 and -1 / z) and the continued fraction with even partial quotients. Using thermodynamic formalism, Tauberian results and the above-mentioned relation, we obtain the asymptotic growth number of closed trajectories for the theta group. Several results for the continued fraction expansion with even partial quotients are obtained; some of these are analogous to those already known for the usual continued fraction expansion related to the modular group, but our proofs are by necessity in general technically more difficult. |
| Starting Page | 293 |
| Ending Page | 333 |
| Page Count | 41 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/BF00181695 |
| Alternate Webpage(s) | http://mat.ufrgs.br/~alopes/kra.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/BF00181695 |
| Volume Number | 59 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
