Symmetry of hypergeometric functions over finite fields and geometric interpretation

Akio Nakagawa

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arXiv · 2505.05858

Symmetry of hypergeometric functions over finite fields and geometric interpretation

Akio Nakagawa

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Abstract

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms between certain algebraic varieties. The numbers of rational points on these varieties are hypergeometric functions over finite fields.

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Akio Nakagawa. 2025-05-09. Symmetry of hypergeometric functions over finite fields and geometric interpretation. https://arxiv.org/abs/2505.05858

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