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
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.
Recommended Citation
Griffin, Elise and Malmendier, Andreas, "Jacobian Elliptic Kummer Surfaces and Special Function Identities" (2018). Mathematics and Statistics Faculty Publications. Paper 228.
https://digitalcommons.usu.edu/mathsci_facpub/228
