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Congruent Number Theta Coefficients to 1012

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Algorithmic Number Theory (ANTS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6197))

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Abstract

We report on a computation of congruent numbers, which subject to the Birch and Swinnerton-Dyer conjecture is an accurate list up to 1012. The computation involves multiplying long theta series as per Tunnell (1983). The method, which we describe in some detail, uses a multimodular disk based technique for multiplying polynomials out-of-core which minimises expensive disk access by keeping data truncated.

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Author information

Authors and Affiliations

  1. Mathematics Institute, Warwick University, Coventry, United Kingdom

    William B. Hart

  2. Centro de Matemática, Universidad de la República, Montevideo, Uruguay

    Gonzalo Tornaría

  3. Department of Mathematics and Statistics, University of Sydney, Australia

    Mark Watkins

Authors
  1. William B. Hart
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  2. Gonzalo Tornaría
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  3. Mark Watkins
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Editor information

Editors and Affiliations

  1. LIP/ENS-Lyon, 46, allée d’Italie, 69364, Lyon, Cedex 07, France

    Guillaume Hanrot

  2. Laboratoire d’Informatique (CNRS/UMR 7650), École polytechnique, 91128, Palaiseau Cedex, France

    François Morain

  3. INRIA Nancy, project CARAMEL, 615 rue du jardin botanique, 54602, Villers-lès-Nancy Cedex,, France

    Emmanuel Thomé

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Hart, W.B., Tornaría, G., Watkins, M. (2010). Congruent Number Theta Coefficients to 1012 . In: Hanrot, G., Morain, F., Thomé, E. (eds) Algorithmic Number Theory. ANTS 2010. Lecture Notes in Computer Science, vol 6197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14518-6_17

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  • DOI: https://doi.org/10.1007/978-3-642-14518-6_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14517-9

  • Online ISBN: 978-3-642-14518-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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