Evaluations of hypergeometric functions over finite fields
type: Item
instance of: scholarly article
title: Evaluations of hypergeometric functions over finite fields
zbMATH Open document ID: 1241.11138
author: John Greene
author: Ron Evans
published in: Hiroshima Mathematical Journal
publication date: 2009-10-12T00:00:00Z
review text: The authors continue their previous study and prove two general formulas for a two-parameter family of hypergeometric \({}_3F_2(z)\) functions over a finite field \(\mathbb F_q\), where \(q\) is a power of an odd prime. Each formula evaluates a \({}_3F_2\) in terms of a \({}_2F_1\) over \(\mathbb F_{q^2}\). As applications, they evaluate infinite one-parameter families of \({}_3F_2(\frac{1}{4})\) and \({}_3F_2(-1)\), thereby extending results of \textit{J. Greene} and \textit{D. Stanton} [J. Number Theory 23, 136--148 (1986; Zbl 0588.10038)] and \textit{K. Ono}, Trans. Am. Math. Soc. 350, No. 3, 1205--1223 (1998; Zbl 0910.11054)], who gave evaluations in special cases.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 11T24
Mathematics Subject Classification ID: 11L05
Mathematics Subject Classification ID: 33C20
zbMATH DE Number: 5613989
zbMATH Keywords: Hypergeometric functions over finite fields
zbMATH Keywords: Gauss sums
zbMATH Keywords: Jacobi sums
zbMATH Keywords: Davenport--Hasse formulas
zbMATH Keywords: lifted characters
zbMATH Keywords: Stickelberger's congruence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1249046338
OpenAlex ID: W1498968422
Wikidata QID: Q128869116
DOI: 10.32917/HMJ/1249046338
Recommended article: Evaluation of certain hypergeometric functions over finite fields
Recommended article: Hypergeometric functions over finite fields
Recommended article: Hypergeometric Functions Over Finite Fields
Recommended article: Special values of hypergeometric functions over finite fields
Recommended article: Hypergeometric functions over finite fields.
Recommended article: Hypergeometric polynomials over finite fields
Recommended article: Hypergeometric functions for function fields
Recommended article: Kampé de Fériet hypergeometric functions over finite fields
Recommended article: HYPERGEOMETRIC FUNCTIONS OVER FINITE FIELDS AND THEIR RELATIONS TO ALGEBRAIC CURVES
description: scientific article; zbMATH DE number 5613989