3F2 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
JournalInternational Journal of Number Theory
DOIs
StatePublished - May 2010

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