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

Kensaku Kinjo, Yuken Miyasaka

Research output: Contribution to journalArticlepeer-review

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 ≥ 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.

Original languageEnglish
Pages (from-to)831-844
Number of pages14
JournalInternational Journal of Number Theory
Volume8
Issue number3
DOIs
Publication statusPublished - 2012 May 1

Keywords

  • arithmeticgeometric mean
  • p-Adic hypergeometric differential equation
  • unit root of an elliptic curve

ASJC Scopus subject areas

  • Algebra and Number Theory

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