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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.


Evaluating modular forms on Shimura curves
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by Paul D. Nelson PDF
Math. Comp. 84 (2015), 2471-2503 Request permission


Let $f$ be a newform, as specified by its Hecke eigenvalues, on a Shimura curve $X$. We describe a method for evaluating $f$. The most interesting case is when $X$ arises as a compact quotient of the hyperbolic plane, so that classical $q$-expansions are not available. The method takes the form of an explicit, rapidly-convergent formula that is well-suited for numerical computation. We apply it to the problem of computing modular parametrizations of elliptic curves, and illustrate with some numerical examples.

An important ingredient is a new method for numerically computing Petersson inner products, which may be of independent interest.

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Additional Information
  • Paul D. Nelson
  • Affiliation: EPFL, Station 8, CH-1015 Lausanne, Switzerland
  • Address at time of publication: ETH Zurich, Raemistrasse 101, 8092 Zurich, Switzerland
  • Email:
  • Received by editor(s): October 9, 2012
  • Received by editor(s) in revised form: October 10, 2013
  • Published electronically: January 23, 2015
  • Additional Notes: The author was supported by NSF grant OISE-1064866 and partially supported by grant SNF-137488 during the completion of this paper.
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2471-2503
  • MSC (2010): Primary 11F11, 11Y40; Secondary 11F27
  • DOI:
  • MathSciNet review: 3356036