A quadratic hypergeometric ₂𝐹₁ transformation over finite fields

DOI10.1090/proc/13303zbMath1403.11079arXiv1511.00020OpenAlexW2963308193MaRDI QIDQ3181317

John Greene, Ronald J. Evans

Publication date: 29 December 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.00020

zbMATH Keywords

Gauss sumsJacobi sumsquadratic transformationsHasse-Davenport relationhypergeometric \(_2F_1\) functions over finite fieldspseudo-hypergeometric functions

Mathematics Subject Classification ID

Other character sums and Gauss sums (11T24) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (11)

Some mixed character sum identities of Katz ⋮ AGM and Jellyfish Swarms of Elliptic Curves ⋮ Certain product formulas and values of Gaussian hypergeometric series ⋮ Appell series over finite fields and modular forms ⋮ Some mixed character sum identities of Katz. II ⋮ Hypergeometric functions over finite fields ⋮ Hypergeometric functions over finite fields ⋮ 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 ⋮ Certain transformations and special values of hypergeometric functions over finite fields

Cites Work

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• Traces of Hecke operators in level 1 and Gaussian hypergeometric functions
• CERTAIN VALUES OF GAUSSIAN HYPERGEOMETRIC SERIES AND A FAMILY OF ALGEBRAIC CURVES
• Gaussian hypergeometric evaluations of traces of Frobenius for elliptic curves
• A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform
• Hypergeometric Functions Over Finite Fields

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