The theta group and the continued fraction expansion with even partial quotients
 Cornelis Kraaikamp,
 Artur Lopes
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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 abovementioned 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.
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 Title
 The theta group and the continued fraction expansion with even partial quotients
 Journal

Geometriae Dedicata
Volume 59, Issue 3 , pp 293333
 Cover Date
 19960301
 DOI
 10.1007/BF00181695
 Print ISSN
 00465755
 Online ISSN
 15729168
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 58F11
 Riemann surfaces
 Fuchsian groups
 continued fraction expansion
 thermodynamic formalism
 even partial quotients
 Industry Sectors
 Authors

 Cornelis Kraaikamp ^{(1)}
 Artur Lopes ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Technical University Delft, Mekelweg 4, 2628 CD, Delft, The Netherlands
 2. Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Av.Bento Gonçalves, 9500, 91500, Porto Alegre, RS, Brazil