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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.

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Article copyright: © Copyright 1992 American Mathematical Society