Hypergeometric functions over finite fields satisfy a classical-style symmetry, proven by constructing isomorphisms between algebraic varieties whose rational point counts equal the functions.
Nakagawa, Sum representations of Appell-Lauricella functions over finite fields using con- fluent hypergeometric functions and their applications, Res
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Symmetry of hypergeometric functions over finite fields and geometric interpretation
Hypergeometric functions over finite fields satisfy a classical-style symmetry, proven by constructing isomorphisms between algebraic varieties whose rational point counts equal the functions.