Hypergeometric series and periods of elliptic curves

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Abstract

We express the real period of a family of elliptic curves in terms of classical hypergeometric series. This expression is analogous to a result of Ono which relates the trace of Frobenius of the same family of elliptic curves to a Gaussian hypergeometric series. This analogy provides further evidence of the interplay between classical and Gaussian hypergeometric series.

Original languageEnglish
Pages (from-to)461-470
Number of pages10
JournalInternational Journal of Number Theory
Volume6
Issue number3
DOIs
StatePublished - May 2010

Keywords

  • Elliptic curves
  • Gaussian hypergeometric series
  • Hypergeometric series
  • Real period
  • Trace of Frobenius

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