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A quadratic hypergeometric 2F1 transformation over finite fields

In 1984, the second author conjectured a quadratic transformation formula which relates two hypergeometric 2F1 functions over a finite field F_q. We prove this conjecture and give an application. The proof depends on a new linear transformation formula for pseudo hypergeometric functions over F_q.

preprint2016arXivOpen access
Ron EvansJohn Greene
math.NT
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Ron EvansJohn Greene

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