p-Adic Addition

  • Serge Lang
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 231)


In this chapter we investigate addition on the elliptic curve in relation to divisibility properties of the denominators of its coordinates, and the quadraticity of the additional formula. This takes place in the general framework that a Lie group has an exponential map convergent near the origin, and giving one-parameter analytic subgroups. We want to see what happens when the base field is p-adic. As before, we carry out the theory ad hoc in a simple manner, making use of the addition formulas given explicitly on the elliptic curve, without fancy language.


Formal Group Elliptic Curve Elliptic Curf Prime Element Good Reduction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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