Gaussian hypergeometric functions and traces of Hecke operators

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The trace of Frobenius of elliptic curves and the p-adic gamma function (2012, background): “Hypergeometric functions over finite fields have been applied to many areas but most interestingly perhaps has been their relationships to modular forms [1, 3, 5, 6, 14, 16, 17, 18] and their use in evaluating the number of points over Fp on certain algebraic varieties [1, 5, 14, 20].”
Hypergeometric Series, Truncated Hypergeometric Series, and Gaussian Hypergeometric Functions (2015, methodology): “Gaussian hypergeometric functions have been used to count points on different types of varieties over Fq and they are related to coefficients of various modular forms [22, 31, 15, 16, 23, 34, 6, 1].”
Trace formulas for Hecke operators, Gaussian hypergeometric functions, and the modularity of a threefold (2011, background): “One can also use these results to prove “inductive trace formulas” as in [6, 5].”
Hypergeometric functions over F_p and relations to elliptic curves and modular forms (2008, methodology): “Acknowledgments The author thanks her advisor M. Papanikolas for his advice and support during the preparation of this paper.”