In the 1980's, Greene defined {\it hypergeometric functions over finite fields} using Jacobi
sums. The framework of his theory establishes that these functions possess many properties …

We establish the supercongruences for the fourteen rigid hypergeometric Calabi–Yau
threefolds over Q conjectured by Rodriguez-Villegas in 2003. Our first method is based on …

In this article, we obtain finite field analogues of classical summation identities connecting F
3-Appell series and 4 F 3-classical hypergeometric series. As an application, we establish a …

In this paper, we investigate the relationships among hypergeometric series, truncated
hypergeometric series, and Gaussian hypergeometric functions through some families of …

In this article, we express the special values of F 4⁎, a finite field analogue of the classical
Appell series F 4, in terms of the Fourier coefficients of weight three modular forms. These …

Although links between values of finite field hypergeometric functions and eigenvalues of
elliptic modular forms are well known, we establish in this paper that there are also …

In this article, we find finite field analogues of certain identities satisfied by the classical 4 F 3-
hypergeometric series and Appell series. As an application, we find new summation and …

We prove a supercongruence modulo p3 between the pth Fourier coefficient of a weight 6
modular form and a truncated 6F5-hypergeometric series. Novel ingredients in the proof are …

We provide a formula for the number of F _ p F p-points on the Dwork hypersurface x_1^ n+
x_2^ n ⋯+ x_n^ nn λ\, x_1 x_2 ... x_n= 0 x 1 n+ x 2 n⋯+ xnn-n λ x 1 x 2… xn= 0 in terms of ap …

The number of points on a certain one parameter family of algebraic surface over a finite
field $\F_p $ can be expressed as $ p^ 2+ A_p (\lambda), $ where $ A_p (\lambda) $ is a …