Hypergeometric $\mathbf {{}_3{\it F}_2(1/4)}$ evaluations over finite fields and Hecke eigenforms
type: Item
instance of: scholarly article
title: Hypergeometric $\mathbf {{}_3{\it F}_2(1/4)}$ evaluations over finite fields and Hecke eigenforms
zbMATH Open document ID: 1268.11158
DOI: 10.1090/S0002-9939-09-10091-6
published in: Proceedings of the American Mathematical Society
publication date: 2010-03-08T00:00:00Z
Mathematics Subject Classification ID: 11T24
Mathematics Subject Classification ID: 33E50
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11L05
zbMATH DE Number: 5678516
zbMATH Keywords: hypergeometric functions over finite fields
zbMATH Keywords: Kloosterman sums
zbMATH Keywords: Gauss and Jacobi sums
zbMATH Keywords: Hecke eigenvalues
zbMATH Keywords: Hecke eigenforms
zbMATH Keywords: symmetric power
zbMATH Keywords: Kloosterman sheaf
zbMATH Keywords: Frobenius map
author: Ron Evans
describes a project that uses: SageMath
MaRDI profile type: Publication
cites work: Modularity of a certain Calabi-Yau threefold
cites work: A Gaussian hypergeometric series evaluation and Apéry number congruences
cites work: Q4382830
cites work: La conjecture de Weil. II
cites work: Seventh power moments of Kloosterman sums
cites work: Clausen's theorem and hypergeometric functions over finite fields
cites work: Evaluations of hypergeometric functions over finite fields
cites work: Special values of hypergeometric functions over finite fields
cites work: Q4663129
cites work: L-functions for symmetric products of Kloosterman sums
cites work: Trivial factors for \(L\)-functions of symmetric products of Kloosterman sheaves
cites work: \(L\)-functions of symmetric products of the Kloosterman sheaf over \(Z\)
cites work: Functional equations of $L$-functions for symmetric products of the Kloosterman sheaf
cites work: Hypergeometric Functions Over Finite Fields
cites work: The modularity of the Barth-Nieto quintic and its relatives
cites work: Q4350164
cites work: Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
cites work: Hypergeometric series over finite fields and Apéry numbers
cites work: On the cubes of Kloosterman sums
cites work: Twisted higher moments of Kloosterman sums
cites work: Motivic orthogonal two-dimensional representations of \(\text{Gal}(\overline\mathbb{Q}/\mathbb{Q})\)
cites work: Supercongruences for truncated _{𝑛+1}𝐹_{𝑛} hypergeometric series with applications to certain weight three newforms
cites work: Values of Gaussian hypergeometric series
cites work: Q4449110
cites work: Congruences for \({}_3F_2\) hypergeometric functions over finite fields
cites work: Q4013269
full work available at URL: s0002-9939-09-10091-6
OpenAlex ID: W1487378383
description: scientific article; zbMATH DE number 5678516