Abstract
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.
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© 1978 Springer-Verlag Berlin Heidelberg
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Lang, S. (1978). p-Adic Addition. In: Elliptic Curves. Grundlehren der mathematischen Wissenschaften, vol 231. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07010-9_3
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DOI: https://doi.org/10.1007/978-3-662-07010-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05717-5
Online ISBN: 978-3-662-07010-9
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