For the purposes of this paper supercongruences are congruences between terminating
hypergeometric series and quotients of p-adic Gamma functions that are stronger than those …

Building on the developments of many people including Evans, Greene, Katz, McCarthy,
Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type …

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 consider the congruences modulo p 2 for the truncated hypergeometric functions. For
example, for any odd prime p and two p-integers α, β, we have the congruence …

Let n≥ 3 be an integer and p be a prime with p≡ 1 (mod n). In this paper, we show that n F
n-1 [n-1 nn-1 n… n-1 n 1… 1| 1] p-1≡-Γ p (1 n) n (mod p 3), where the truncated …

Let ℤ p denote the ring of all p-adic integers and call 𝒰={(x 1,…, xn): a 1⁢ x 1+…+ an⁢ xn+
b= 0} a hyperplane over ℤ pn, where at least one of a 1,…, an is not divisible by p. We prove …

We prove two single-parameter q-supercongruences which were recently conjectured by
Guo, and establish their further extensions with one more parameter. Crucial ingredients in …

We give an expression for number of points for the family of Dwork K3 surfaces over finite
fields of order q≡ 1 (mod 4) in terms of Greene's finite field hypergeometric functions. We …

We give aq-analogue of a supercongruence of Deines–Fuselier–Long–Swisher–Tu by
using the 'creative microscoping'method and Gasper's Karlsson–Minton type summation. As …