Gauss’s 2f1 Hypergeometric Function and the Congruent Number Elliptic Curve
نویسندگان
چکیده
Gauss’s hypergeometric function gives a modular parameterization of period integrals of elliptic curves in Legendre normal form E(λ) : y = x(x− 1)(x− λ). We study a modular function which “measures” the variation of periods for the isomorphic curves E(λ) and E ( λ λ−1 ) , and we show that it padically “interpolates” the cusp form for the “congruent number” curve E(2), the case where these pairs collapse to a single curve.
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