$_3F_2$ hypergeometric series and periods of elliptic curves

Dermot McCarthy

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arXiv · 0906.4508

$_3F_2$ hypergeometric series and periods of elliptic curves

Dermot McCarthy

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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.

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Dermot McCarthy. 2009-06-24. $_3F_2$ hypergeometric series and periods of elliptic curves. https://arxiv.org/abs/0906.4508

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