$_3F_2$ hypergeometric series and periods of elliptic curves

Details $_3F_2$ hypergeometric series and periods of elliptic curves $_3F_2$ hypergeometric series and periods of elliptic curves

2009-06-24

arxiv.org/abs/0906.4508v1

Int. J. Number Theory 6 (2010), no. 3, 461-470

Mathematics

Number Theory

9 pages, to appear in the International Journal of Number Theory

Scientific paper

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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