TY - JOUR
T1 - Coding of geodesics on some modular surfaces and applications to odd and even continued fractions
AU - Boca, Florin P.
AU - Merriman, Claire
N1 - Publisher Copyright:
© 2018 Royal Dutch Mathematical Society (KWG)
PY - 2018/10
Y1 - 2018/10
N2 - The connection between geodesics on the modular surface PSL(2,Z)∖H and regular continued fractions, established by Series, is extended to a connection between geodesics on Γ∖H and odd and grotesque continued fractions, where Γ≅Z3∗Z3 is the index two subgroup of PSL(2,Z) generated by the order three elements 0−111 and 01−11, and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on Θ∖H and even continued fractions is discussed in our framework, where Θ denotes the Theta subgroup of PSL(2,Z) generated by 0−110 and 1201.
AB - The connection between geodesics on the modular surface PSL(2,Z)∖H and regular continued fractions, established by Series, is extended to a connection between geodesics on Γ∖H and odd and grotesque continued fractions, where Γ≅Z3∗Z3 is the index two subgroup of PSL(2,Z) generated by the order three elements 0−111 and 01−11, and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on Θ∖H and even continued fractions is discussed in our framework, where Θ denotes the Theta subgroup of PSL(2,Z) generated by 0−110 and 1201.
KW - Even continued fractions
KW - Geodesics coding
KW - Modular surface
KW - Odd continued fractions
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U2 - 10.1016/j.indag.2018.05.004
DO - 10.1016/j.indag.2018.05.004
M3 - Article
AN - SCOPUS:85047840808
SN - 0019-3577
VL - 29
SP - 1214
EP - 1234
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
IS - 5
ER -