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Explicit Coleman Integration for Hyperelliptic Curves

  • Jennifer S. Balakrishnan
  • Robert W. Bradshaw
  • Kiran S. Kedlaya
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jennifer S. Balakrishnan
    • 1
  • Robert W. Bradshaw
    • 2
  • Kiran S. Kedlaya
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.University of WashingtonSeattleUSA

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