105 citations · 168 across the 35 of their papers we have counts for
8 papers · 1 filter
An extension of a supercongruence of Long and Ramakrishna
Victor J. W. Guo, Ji-Cai Liu, Michael J. Schlosser
We prove two supercongruences for specific truncated hypergeometric series. These include an uniparametric extension of a supercongruence that was recently established by Long and…
A -adic analogue of Chan and Verrill's formula for
Ji-Cai Liu
We prove three supercongruences for sums of Almkvist-Zudilin numbers, which confirm some conjectures of Zudilin and Z.-H. Sun. A typical example is the Ramanujan-type supercongruen…
Supercongruences for sums involving Domb numbers
Ji-Cai Liu
We prove some supercongruence and divisibility results on sums involving Domb numbers, which confirm four conjectures of Z.-W. Sun and Z.-H. Sun. For instance, by using a transform…
Supercongruences for Almkvist--Zudilin sequences
Ji-Cai Liu, He-Xia Ni
In this note, we prove two supercongruences involving Almkvist--Zudilin sequences, which were originally conjectured by Z.-H. Sun.
A Remark on stress of a spatially uniform dislocation density field
Siran Li
In an interesting recent paper [1] (A. Acharya, Stress of a spatially uniform dislocation density field, J. Elasticity 137 (2019), 151--155), Acharya proved that the stress produce…
A variation of -Wolstenholme's theorem
Ji-Cai Liu
We investigate a variation of -Wolstenholme's theorem, which extends the -analogue of Wolstenholme's theorem due to Shi and Pan [Amer. Math. Monthly 114 (2007), 529--531]. Th…
On two congruences involving Franel numbers
Ji-Cai Liu
Via symbolic summation method, we establish the following series for : \begin{align*} \sum_{k=1}^\infty \frac{H_k-2H_{2k}}{(-3)^k k} = \frac{π^2}{18}, \end{align*} where $H_k=…
Proof of Sun's supercongruence involving Catalan numbers
Ji-Cai Liu
We confirm a conjectural supercongruence involving Catalan numbers, which is one of the 100 selected open conjectures on congruences of Sun. The proof makes use of hypergeometric s…