## On the computational complexity of modular symbols

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- by Dorian Goldfeld PDF
- Math. Comp.
**58**(1992), 807-814 Request permission

## 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

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## Additional Information

- © Copyright 1992 American Mathematical Society
- Journal: Math. Comp.
**58**(1992), 807-814 - MSC: Primary 11F67; Secondary 11Y35
- DOI: https://doi.org/10.1090/S0025-5718-1992-1122069-5
- MathSciNet review: 1122069