Hypergeometric series and arithmetic-geometric mean over 2-adic fields

Kensaku Kinjo, Yuken Miyasaka

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)831-844
ページ数14
ジャーナルInternational Journal of Number Theory
8
3
DOI
出版ステータスPublished - 2012 5

ASJC Scopus subject areas

  • 代数と数論

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