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

On the computational complexity of modular symbols


Author: Dorian Goldfeld
Journal: Math. Comp. 58 (1992), 807-814
MSC: Primary 11F67; Secondary 11Y35
MathSciNet review: 1122069
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Abstract: Efficient algorithms are obtained for integrating holomorphic differential one-forms along simple geodesic lines on those compact Riemann surfaces which are given as quotients of the upper half-plane by a congruence subgroup $ \Gamma $ of $ {\text{SL}}(2,\mathbb{Z})$. We may assume that every geodesic line passes through a cusp which is unique up to $ \Gamma $-equivalence. The algorithms we construct run in polynomial time in the height of this cusp.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1122069-5
PII: S 0025-5718(1992)1122069-5
Article copyright: © Copyright 1992 American Mathematical Society