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Number Theory Seminar
Seminar information archive ～09/19｜Next seminar｜Future seminars 09/20～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2011/11/02
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Kensaku Kinjo (University of Tokyo)
Hypergeometric series and arithmetic-geometric mean over 2-adic fields (JAPANESE)
Kensaku Kinjo (University of Tokyo)
Hypergeometric series and arithmetic-geometric mean over 2-adic fields (JAPANESE)
[ Abstract ]
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>2.
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 arithmetic-geometric mean.
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>2.
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 arithmetic-geometric mean.
