Evaluations of hypergeometric functions over finite fields

Ron Evans, John Greene

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We prove two general formulas for a two-parameter family of hypergeometric 3F2(z) functions over a finite field Fq, where q is a power of an odd prime. Each formula evaluates a 3F2 in terms of a 2F1 over Fq2 As applications, we evaluate infinite one-parameter families of 3F2(1/4) and 3F2(-1), thereby extending results of J. Greene-D. Stanton and K. Ono, who gave evaluations in special cases.

Original languageEnglish (US)
Pages (from-to)217-235
Number of pages19
JournalHiroshima Mathematical Journal
Volume39
Issue number2
DOIs
StatePublished - 2009

Keywords

  • Davenport-Hasse formulas
  • Gauss sums
  • Hypergeometric functions over finite fields
  • Jacobi sums
  • Lifted characters
  • Stickelberger's congruence

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