Document Type

Article

Journal/Book Title/Conference

Communications in Number Theory and Physics

Volume

12

Issue

1

Publication Date

4-27-2018

First Page

1

Last Page

20

DOI

http://dx.doi.org/10.4310/CNTP.2018.v12.n1.a4

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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