## Abstract

In 1984, the second author conjectured a quadratic transformation formula which relates two hypergeometric_{2}F_{1} functions over a finite field F_{q}. We prove this conjecture in Theorem 2. The proof depends on a new linear transformation formula for pseudo-hypergeometric functions over F_{q}. Theorem 2 is then applied to give an elegant new transformation formula (Theorem 3) for_{2}F_{1} functions over finite fields.

Original language | English (US) |
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Pages (from-to) | 1071-1076 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 145 |

Issue number | 3 |

DOIs | |

State | Published - 2017 |

### Bibliographical note

Publisher Copyright:© 2016 American Mathematical Society.

## Keywords

- Gauss sums
- Hasse–Davenport relation
- Hypergeometric F functions over finite fields
- Jacobi sums
- Pseudo-hypergeometric functions
- Quadratic transformations

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