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, Appell-Lauricella hypergeometric functions over finite fields and algebraic va- rieties, Hokkaido Math
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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.