On the computational complexity of modular symbols
Author:
Dorian Goldfeld
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
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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
