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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computing self-intersections of closed geodesics on finite-sheeted covers of the modular surface
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by J. Lehner and M. Sheingorn PDF
Math. Comp. 44 (1985), 233-240 Request permission


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
  • © Copyright 1985 American Mathematical Society
  • Journal: Math. Comp. 44 (1985), 233-240
  • MSC: Primary 11F06; Secondary 11J06, 20H10, 30F35
  • DOI:
  • MathSciNet review: 771045