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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.


Elementary matrix decomposition and the computation of Darmon points with higher conductor
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by Xavier Guitart and Marc Masdeu PDF
Math. Comp. 84 (2015), 875-893 Request permission


We extend the algorithm of Darmon–Green and Darmon–Pollack for computing $p$-adic Darmon points on elliptic curves to the case of composite conductor. We also extend the algorithm of Darmon–Logan for computing ATR Darmon points to treat curves of nontrivial conductor. Both cases involve an algorithmic decomposition into elementary matrices in congruence subgroups $\Gamma _1({\mathfrak N})$ for ideals ${\mathfrak N}$ in certain rings of $S$-integers. We use these extensions to provide additional evidence in support of the conjectures on the rationality of Darmon points.
  • H. Bass, J. Milnor, and J.-P. Serre. Solution of the congruence subgroup problem for $\textrm {SL}_{n}\,(n\geq 3)$ and $\textrm {Sp}_{2n}\,(n\geq 2)$. Inst. Hautes Études Sci. Publ. Math., (33):59–137, 1967.
  • George Cooke and Peter J. Weinberger, On the construction of division chains in algebraic number rings, with applications to $\textrm {SL}_{2}$, Comm. Algebra 3 (1975), 481–524. MR 387251, DOI 10.1080/00927877508822057
  • Henri Darmon, Integration on $\scr H_p\times \scr H$ and arithmetic applications, Ann. of Math. (2) 154 (2001), no. 3, 589–639. MR 1884617, DOI 10.2307/3062142
  • Henri Darmon, Rational points on modular elliptic curves, CBMS Regional Conference Series in Mathematics, vol. 101, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2004. MR 2020572
  • Henri Darmon and Peter Green, Elliptic curves and class fields of real quadratic fields: algorithms and evidence, Experiment. Math. 11 (2002), no. 1, 37–55. MR 1960299
  • Henri Darmon and Adam Logan, Periods of Hilbert modular forms and rational points on elliptic curves, Int. Math. Res. Not. 40 (2003), 2153–2180. MR 1997296, DOI 10.1155/S1073792803131108
  • Henri Darmon and Robert Pollack, Efficient calculation of Stark-Heegner points via overconvergent modular symbols, Israel J. Math. 153 (2006), 319–354. MR 2254648, DOI 10.1007/BF02771789
  • Jérôme Gärtner, Points de Darmon et variétés de Shimura, 2011. Ph.D. Thesis, Institut de Mathématiques de Jussieu.
  • Xavier Guitart and Marc Masdeu, Computation of ATR Darmon points on nongeometrically modular elliptic curves, Exp. Math. 22 (2013), no. 1, 85–98. MR 3038785, DOI 10.1080/10586458.2013.738564
  • Matthew Greenberg, Heegner points and rigid analytic modular forms, ProQuest LLC, Ann Arbor, MI, 2006. Thesis (Ph.D.)–McGill University (Canada). MR 2710023
  • L. N. Vaseršteĭn, The group $SL_{2}$ over Dedekind rings of arithmetic type, Mat. Sb. (N.S.) 89(131) (1972), 313–322, 351 (Russian). MR 0435293
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Additional Information
  • Xavier Guitart
  • Affiliation: Universitat Politècnica de Catalunya, Departament de Matematica Aplicada II, C/Jordi Girona, 1-3, 08034 Barcelona (Spain)
  • MR Author ID: 887813
  • Email:
  • Marc Masdeu
  • Affiliation: Columbia University, Department of Mathematics, Room 415, MC 4441, 2990 Broadway, New York, New York 10027
  • MR Author ID: 772165
  • Email:
  • Received by editor(s): May 14, 2013
  • Received by editor(s) in revised form: June 5, 2013
  • Published electronically: July 17, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 84 (2015), 875-893
  • MSC (2010): Primary 11G40; Secondary 11F41, 11Y99
  • DOI:
  • MathSciNet review: 3290967