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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.


Explicit Coleman integration for curves
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by Jennifer S. Balakrishnan and Jan Tuitman HTML | PDF
Math. Comp. 89 (2020), 2965-2984 Request permission


The Coleman integral is a $p$-adic line integral that plays a key role in computing several important invariants in arithmetic geometry. We give an algorithm for explicit Coleman integration on curves, using the algorithms of the second author [Math. Comp. 85 (2016), pp. 961–981] and [Finite Fields Appl. 45 (2019), pp. 301–322] to compute the action of Frobenius on $p$-adic cohomology. We present a collection of examples computed with our implementation. This includes integrals on a genus 55 curve, where other methods do not currently seem practical.
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Additional Information
  • Jennifer S. Balakrishnan
  • Affiliation: Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston, Massachusetts 02215
  • MR Author ID: 910890
  • Email:
  • Jan Tuitman
  • Affiliation: Departement Wiskunde, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
  • MR Author ID: 941045
  • Email:
  • Received by editor(s): November 14, 2017
  • Received by editor(s) in revised form: January 10, 2020, January 16, 2020, and March 2, 2020
  • Published electronically: May 22, 2020
  • Additional Notes: The first author was supported in part by NSF grant DMS-1702196, the Clare Boothe Luce Professorship (Henry Luce Foundation), and Simons Foundation grant #550023.
    The second author is a Postdoctoral Researcher of the Fund for Scientific Research FWO - Vlaanderen.
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 89 (2020), 2965-2984
  • MSC (2010): Primary 11S80; Secondary 11Y35, 11Y50
  • DOI:
  • MathSciNet review: 4136553