105 citations · 168 across the 35 of their papers we have counts for
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A -adic supercongruence for truncated hypergeometric series
Ji-Cai Liu
Using an identity due to Gessel and Stanton and some properties of the -adic Gamma function, we establish a -adic supercongruence for truncated hypergeometric series ${}_7F_6…
Supercongruences involving -adic Gamma functions
Ji-Cai Liu
We establish some supercongruences for the truncated and hypergeometric series involving the -adic Gamma functions. Some of these results extend the four Rod…
Some supercongruences on truncated hypergeometric series
Ji-Cai Liu
In 2003, Rodriguez-Villegas conjectured four supercongruences on the truncated hypergeometric series for certain modular K3 surfaces, which were gradually proved by sever…
On two conjectural supercongruences of Apagodu and Zeilberger
Ji-Cai Liu
Let the numbers and denote \begin{align*} α_n=\sum_{k=0}^{n-1}{2k\choose k},\quad β_n=\sum_{k=0}^{n-1}{2k\choose k}\frac{1}{k+1}\quad\text{and}\quad γ_n=\sum_{k=0}^…
Congruences for truncated hypergeometric series
Ji-Cai Liu
Rodriguez-Villegas conjectured four supercongruences associated to certain elliptic curves, which were first confirmed by Mortenson by using the Gross-Koblitz formula. In this pape…
Proof of some divisibility results on sums involving binomial coefficients
Ji-Cai Liu
By using the Rodriguez-Villegas-Mortenson supercongruences, we prove four supercongruences on sums involving binomial coefficients, which were originally conjectured by Sun. We als…
A supercongruence involving Delannoy numbers and Schröder numbers
Ji-Cai Liu
The Delannoy numbers and Schröder numbers are given by \begin{align*} D_n=\sum_{k=0}^n{n\choose k}{n+k\choose k}\quad \text{and}\quad S_n=\sum_{k=0}^n{n\choose k}{n+k\choose k}\fra…