Based on Ramanujan's theories of elliptic functions to alternative bases, commutative formal
group laws, and supercongruence techniques, including the residue-sum technique, we …

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 …

We give a definition of generalized hypergeometric functions over finite fields using modified
Gauss sums, which enables us to find clear analogy with classical hypergeometric functions …

In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp
forms in certain instances related to arithmetic triangle groups. These expressions are in …

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 …

For a, b, c, d, e∈ Q×, denote by C a, b, c, d, e the nonsingular projective curve over Q given
by the affine equation C a, b, c, d, e: ax 2+ by 2= c+ dxy+ ex 2 y 2. In this paper, we find a …

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 …

We consider the action of the 2-dimensional projective special linear group PSL (2, q) on the
projective line PG (1, q) over the finite field F q, where q is an odd prime power. A subset S of …

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 …