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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computing self-intersections of closed geodesics on finite-sheeted covers of the modular surface


Authors: J. Lehner and M. Sheingorn
Journal: Math. Comp. 44 (1985), 233-240
MSC: Primary 11F06; Secondary 11J06, 20H10, 30F35
MathSciNet review: 771045
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Abstract: An algorithm is given for deciding whether a closed geodesic on a finite-sheeted cover of the modular surface has self-intersections; if it does, the algorithm gives them in the order they occur in traversing the geodesic. The following general result on geodesics is proved: any closed geodesic on a Riemann surface R can be lifted to a simple closed geodesic on some finite-sheeted cover of R. In the last two sections the connection with the stabilizer (under the modular group) of a Markov quadratic irrationality is discussed.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1985-0771045-7
PII: S 0025-5718(1985)0771045-7
Article copyright: © Copyright 1985 American Mathematical Society