Evaluation of Certain Hypergeometric Functions over Finite Fields
Fang-Ting Tu, Yifan Yang

TL;DR
This paper evaluates certain hypergeometric functions over finite fields ${f F}_p$ in terms of Hecke characters linked to CM elliptic curves, for specific character orders, enhancing understanding of their algebraic and arithmetic properties.
Contribution
It provides explicit evaluations of hypergeometric functions over finite fields in terms of Hecke characters associated with CM elliptic curves for specific character orders.
Findings
Explicit formulas for hypergeometric functions over ${f F}_p$
Connections between hypergeometric functions and CM elliptic curves
Evaluation in terms of Hecke characters for orders 3, 4, 6, 8, 12
Abstract
For an odd prime , let denote the quadratic character of the multiplicative group , where is the finite field of elements. In this paper, we will obtain evaluations of the hypergeometric functions , , , over in terms of Hecke character attached to CM elliptic curves for characters of of order , , , , and .
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