Abstract
In 1984, the second author conjectured a quadratic transformation formula which relates two hypergeometric2F1 functions over a finite field Fq. We prove this conjecture in Theorem 2. The proof depends on a new linear transformation formula for pseudo-hypergeometric functions over Fq. Theorem 2 is then applied to give an elegant new transformation formula (Theorem 3) for2F1 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