HYPERGEOMETRIC SERIES AND ARITHMETIC–GEOMETRIC MEAN OVER 2-ADIC FIELDS
2012 ◽
Vol 08
(03)
◽
pp. 831-844
Keyword(s):
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 arithmetic–geometric mean.
1995 ◽
Vol 38
(2)
◽
pp. 167-173
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Keyword(s):
2010 ◽
Vol 53
(1)
◽
pp. 1-12
◽
2019 ◽
Vol 38
(3)
◽
pp. 193-201
◽
Keyword(s):
2009 ◽
Vol 05
(02)
◽
pp. 229-256
◽
Keyword(s):
2012 ◽
Vol 08
(04)
◽
pp. 945-961
◽
Keyword(s):
2016 ◽
Vol 13
(01)
◽
pp. 133-152
2016 ◽
Vol 68
(4)
◽
pp. 721-761
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Keyword(s):