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arXiv · 1609.00111

Jacobian elliptic Kummer surfaces and special function identities

Elise Griffin·Andreas Malmendier
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Abstract

We derive formulas for the construction of all inequivalent Jacobian elliptic fibrations on the Kummer surface of two non-isogeneous elliptic curves from extremal rational elliptic surfaces by rational base transformations and quadratic twists. We then show that each such decomposition yields a description of the Picard-Fuchs system satisfied by the periods of the holomorphic two-form as either a tensor product of two Gauss' hypergeometric differential equations, an Appell hypergeometric system, or a GKZ differential system. As the answer must be independent of the fibration used, identities relating differential systems are obtained. They include a new identity relating Appell's hypergeometric system to a product of two Gauss' hypergeometric differential equations by a cubic transformation.

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Elise Griffin, Andreas Malmendier. 2016-09-01. Jacobian elliptic Kummer surfaces and special function identities. https://doi.org/10.4310/cntp.2018.v12.n1.a4

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