Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures

Dermot McCarthy; Madeline Locus Dawsey

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arxiv 2101.06303 v1 pith:TEUK43NY submitted 2021-01-15 math.NT

Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures

Madeline Locus Dawsey , Dermot McCarthy This is my paper

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keywords finitefunctionshypergeometricfieldsformsmodularalgebraicanalogue

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Hypergeometric functions over finite fields were introduced by Greene in the 1980s as a finite field analogue of classical hypergeometric series. These functions, and their generalizations, naturally lend themselves to, and have been widely used in, character sum evaluations and counting points on algebraic varieties. More interestingly, perhaps, are their links to Fourier coefficients of modular forms. In this paper, we outline the main results in this area and also conjecture 13 new relations.

Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures

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