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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.


A modular approach to cubic Thue-Mahler equations
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by Dohyeong Kim PDF
Math. Comp. 86 (2017), 1435-1471 Request permission


Let $h(x,y)$ be a non-degenerate binary cubic form with integral coefficients, and let $S$ be an arbitrary finite set of prime numbers. By a classical theorem of Mahler, there are only finitely many pairs of relatively prime integers $x,y$ such that $h(x,y)$ is an $S$-unit. In the present paper, we reverse a well-known argument, which seems to go back to Shafarevich, and use the modularity of elliptic curves over $\mathbb {Q}$ to give upper bounds for the number of solutions of such a Thue-Mahler equation. In addition, our methods give an effective method for determining all solutions, and we use Cremonaโ€™s Elliptic Curve Database to give a wide range of numerical examples.
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Additional Information
  • Dohyeong Kim
  • Affiliation: Center for Geometry and Physics, Institute for Basic Science (IBS), 77 Cheongam-ro, Nam-gu, Pohang-si, Gyeongsangbuk-do, 790-784, Republic of Korea โ€“ and โ€“ Pohang University of Science and Technology (POSTECH), 77 Cheongam-ro, Nam-gu, Pohang-si, Gyeongsangbuk-do, 790-784, Republic of Korea
  • Address at time of publication: Department of Mathematics, University of Michigan, 2074 East Hall, Ann Arbor, Michigan 48109-1043
  • MR Author ID: 970842
  • Email:
  • Received by editor(s): June 9, 2015
  • Received by editor(s) in revised form: November 27, 2015
  • Published electronically: September 15, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1435-1471
  • MSC (2010): Primary 11D59, 11F11, 11Y50
  • DOI:
  • MathSciNet review: 3614023