Dwork proved that the Gaussian hypergeometric function on p-adic numbers can be extended to a function which takes values of the unit roots of ordinary elliptic curves over a finite field of characteristic p ≥ 3. We present an analogous theory in the case p = 2. As an application, we give a relation between the canonical lift and the unit root of an elliptic curve over a finite field of characteristic 2 by using the 2-adic arithmeticgeometric mean.
- arithmeticgeometric mean
- p-Adic hypergeometric differential equation
- unit root of an elliptic curve
ASJC Scopus subject areas
- Algebra and Number Theory