A quadratic hypergeometric 2F1 transformation over finite fields

Ron Evans, John Greene

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)1071-1076
Number of pages6
JournalProceedings of the American Mathematical Society
Volume145
Issue number3
DOIs
StatePublished - 2017

Keywords

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

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