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International Algorithmic Number Theory Symposium

ANTS 2010: Algorithmic Number Theory pp 16–31Cite as

Explicit Coleman Integration for Hyperelliptic Curves

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

Abstract

Coleman’s theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage.

Keywords

  • Hyperelliptic Curve
  • Weierstrass Point
  • Torsion Point
  • Multiple Zeta
  • Height Pairing

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Jennifer S. Balakrishnan & Kiran S. Kedlaya

  2. University of Washington, Seattle, WA, 98195, USA

    Robert W. Bradshaw

Authors
  1. Jennifer S. Balakrishnan
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  2. Robert W. Bradshaw
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  3. Kiran S. Kedlaya
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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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Balakrishnan, J.S., Bradshaw, R.W., Kedlaya, K.S. (2010). Explicit Coleman Integration for Hyperelliptic Curves. 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-14518-6_6

  • 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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