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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the computational complexity of modular symbols
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by Dorian Goldfeld PDF
Math. Comp. 58 (1992), 807-814 Request permission


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.
  • A. O. L. Atkin and J. Lehner, Hecke operators on $\Gamma _{0}(m)$, Math. Ann. 185 (1970), 134–160. MR 268123, DOI 10.1007/BF01359701
  • J. E. Cremona, Computation of modular elliptic curves and the Birch-Swinnerton Dyer conjecture, preprint.
  • Dorian Goldfeld, Modular elliptic curves and Diophantine problems, Number theory (Banff, AB, 1988) de Gruyter, Berlin, 1990, pp.Β 157–175. MR 1106659
  • P. T. Lockhart, Diophantine equations and the arithmetic of hyperelliptic curves, Ph.D. Thesis, Columbia University, 1990.
  • Ju. I. Manin, Parabolic points and zeta functions of modular curves, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), 19–66 (Russian). MR 0314846
  • Goro Shimura, Introduction to the arithmetic theory of automorphic functions, KanΓ΄ Memorial Lectures, No. 1, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Publications of the Mathematical Society of Japan, No. 11. MR 0314766
  • Goro Shimura, On the factors of the jacobian variety of a modular function field, J. Math. Soc. Japan 25 (1973), 523–544. MR 318162, DOI 10.2969/jmsj/02530523
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 807-814
  • MSC: Primary 11F67; Secondary 11Y35
  • DOI:
  • MathSciNet review: 1122069