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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.


Algorithms for Chow-Heegner points via iterated integrals
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by Henri Darmon, Michael Daub, Sam Lichtenstein and Victor Rotger PDF
Math. Comp. 84 (2015), 2505-2547 Request permission


Let $E_{/\mathbf Q}$ be an elliptic curve of conductor $N$ and let $f$ be the weight $2$ newform on $\Gamma _0(N)$ associated to it by modularity. Building on an idea of S. Zhang, an article by Darmon, Rotger, and Sols describes the construction of so-called Chow-Heegner points, $P_{T,f}\in E({\bar {\mathbf Q}})$, indexed by algebraic correspondences $T\subset X_0(N)\times X_0(N)$. It also gives an analytic formula, depending only on the image of $T$ in cohomology under the complex cycle class map, for calculating $P_{T,f}$ numerically via Chen’s theory of iterated integrals. The present work describes an algorithm based on this formula for computing the Chow-Heegner points to arbitrarily high complex accuracy, carries out the computation for all elliptic curves of rank $1$ and conductor $N< 100$ when the cycles $T$ arise from Hecke correspondences, and discusses several important variants of the basic construction.
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Additional Information
  • Henri Darmon
  • Affiliation: Department of Mathematics, McGill University, Montreal, Canada
  • MR Author ID: 271251
  • Email:
  • Michael Daub
  • Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California
  • Email:
  • Sam Lichtenstein
  • Affiliation: University of California at Stanford, Stanford, California
  • Email:
  • Victor Rotger
  • Affiliation: Department of Mathematics, Universitat Politècnica de Catalunya, Barcelona, Spain
  • MR Author ID: 698263
  • Email:
  • Received by editor(s): December 23, 2011
  • Received by editor(s) in revised form: October 28, 2013, and December 23, 2013
  • Published electronically: March 2, 2015

  • Dedicated: With an appendix by William Stein
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2505-2547
  • MSC (2010): Primary 11F67, 11G05, 11Y16, 14C15
  • DOI:
  • MathSciNet review: 3356037