Hypergeometric functions and elliptic curves (Q861559)

In this article, the author suggests a correspondence between hypergeometric functions and Gaussian hypergeometric functions. As evidences of the correspondence, he shows, for elliptic curves \(E\) given in Legendre normal form, the analogy between an expression of the real period of \(E\) in terms of a classical hypergeometric function and an expression of the trace of Frobenius of \(E\) in terms of a Gaussian hypergeometric function.