Evaluations of hypergeometric functions over finite fields

DOI10.32917/hmj/1249046338zbMath1241.11138OpenAlexW1498968422MaRDI QIDQ730692

John Greene, Ronald J. Evans

Publication date: 12 October 2009

Published in: Hiroshima Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.32917/hmj/1249046338

zbMATH Keywords

Gauss sumsJacobi sumsDavenport--Hasse formulasHypergeometric functions over finite fieldslifted charactersStickelberger's congruence

Mathematics Subject Classification ID

Gauss and Kloosterman sums; generalizations (11L05) Other character sums and Gauss sums (11T24) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (14)

Evaluation of certain hypergeometric functions over finite fields ⋮ A quadratic hypergeometric ₂𝐹₁ transformation over finite fields ⋮ Certain product formulas and values of Gaussian hypergeometric series ⋮ Certain character sums, Gaussian hypergeometric series, and their connections to algebraic curves ⋮ An Appell series over finite fields ⋮ Values of Gaussian hypergeometric series and their connections to algebraic curves ⋮ Certain character sums and hypergeometric series ⋮ Some mixed character sum identities of Katz. II ⋮ Hypergeometric $\mathbf {{}_3{\it F}_2(1/4)}$ evaluations over finite fields and Hecke eigenforms ⋮ Appell series over finite fields and Gaussian hypergeometric series ⋮ Hypergeometric functions over finite fields ⋮ \(_4F_3\)-Gaussian hypergeometric series and traces of Frobenius for elliptic curves ⋮ Summation identities and special values of hypergeometric series in the \(p\)-adic setting ⋮ Certain transformations and special values of hypergeometric functions over finite fields

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