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arXiv · 1711.05842

Evaluation of Certain Hypergeometric Functions over Finite Fields

Fang-Ting Tu·Yifan Yang
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Abstract

For an odd prime $p$, let $ϕ$ denote the quadratic character of the multiplicative group ${\mathbb F}_p^\times$, where ${\mathbb F}_p$ is the finite field of $p$ elements. In this paper, we will obtain evaluations of the hypergeometric functions $ {}_2F_1\left(\begin{matrix} ϕψ& ψ\\ & ϕ\end{matrix};x\right)$, $x\in {\mathbb F}_p$, $x\neq 0, 1$, over ${\mathbb F}_p$ in terms of Hecke character attached to CM elliptic curves for characters $ψ$ of ${\mathbb F}_p^\times$ of order $3$, $4$, $6$, $8$, and $12$.

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Fang-Ting Tu, Yifan Yang. 2018-05-19. Evaluation of Certain Hypergeometric Functions over Finite Fields. https://doi.org/10.3842/sigma.2018.050

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