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Hypergeometric functions and elliptic curves

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Abstract

We provide uniform formulas for the real period and the trace of Frobenius associated to an elliptic curve in Legendre normal form. These are expressed in terms of classical and Gaussian hypergeometric functions, respectively.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706

    Jeremy Rouse

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  1. Jeremy Rouse
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Correspondence to Jeremy Rouse.

Additional information

This research was supported by K. Ono’s NSF grant

2000 Mathematics Subject Classification Primary—11G05, 33C05

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Rouse, J. Hypergeometric functions and elliptic curves. Ramanujan J 12, 197–205 (2006). https://doi.org/10.1007/s11139-006-0073-3

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  • DOI: https://doi.org/10.1007/s11139-006-0073-3

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