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