3 citations · 10 across the 17 of their papers we have counts for
17 papers
Cyclic permutations of large subsets with polynomial values in multiplicative subgroups of finite fields
Hai-Liang Wu, He-Xia Ni
Let be a nonconstant polynomial with nonzero discriminant and let be an integer. Inspired by the work of Alon and Bourgain, for sufficiently large pr…
On the Burgess bound and Pythagorean triples involving primitive roots
Hai-Liang Wu, He-Xia Ni
By combining the recent results of Pierce and Xu on the higher-dimensional Burgess bound with the classical one-dimensional Burgess bound, we prove that for any sufficiently large…
Supercongruences Arising from Truncated Appell Series
He-Xia Ni
In recent years, both Appell series and truncated Appell series have garnered significant research interest among scholars. In this paper, we investigate the congruence properties…
A supercongruence related to Whipple's formula and Dwork's dash operation
Chen Wang, He-Xia Ni
We establish a parametric supercongruence related to Whipple's formula and Dwork's dash operation. As a typical consequence, we obtain the following result: for any prime…
The Pell sequence and cyclotomic matrices involving squares over finite fields
Hai-Liang Wu, Li-Yuan Wang, He-Xia Ni
In this paper, by some arithmetic properties of the Pell sequence and some -adic tools, we study certain cyclotomic matrices involving squares over finite fields. For example, l…
On a generalization of R. Chapman's "evil determinant"
Li-Yuan Wang, Hai-Liang Wu, He-Xia Ni
Let be an odd prime and be an indeterminate. Recently, Z.-W. Sun proposed the following conjecture: $$\det\left[x+\left(\frac{j-i}{p}\right)\right]_{0\le i,j\le \frac{p-1}{…
Some -congruences involving central -binomial coefficients
He-Xia Ni
Suppose that is an odd prime and is an integer not divisible by . Sun and Tauraso [Adv. in Appl. Math., 45(2010), 125--148] gave an…
-Supercongruences from transformation formulas
He-Xia Ni, Li-Yuan Wang, Hai-Liang Wu
Let denote the -th cyclotomic polynomial in . Recently, Guo and Schlosser [Constr. Approx. 53 (2021), 155--200] put forward the following conjecture: for an odd in…
A conjecture of Zhi-Wei Sun on determinants over finite fields
Hai-Liang Wu, Yue-Feng She, He-Xia Ni
In this paper, we study certain determinants over finite fields. Let be the finite field of elements and let be all nonzero elements of…
Two -supercongruences from Watson's transformation
He-Xia Ni, Li-Yuan Wang
Guo and Zudilin [Adv. Math. 346 (2019), 329--358] introduced a new method called `creative microscoping', to prove many -supercongruences in a unified way. In this paper, we app…
A -Dwork-type generalization of Rodriguez-Villegas' supercongruences
He-Xia Ni
Guo and Zudilin [Adv. Math. 346 (2019), 329--358] developed an analytical method, called `creative microscoping', to prove many supercongruences by establishing their -analogues…
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.
Some -congruences arising from certain identities
Chen Wang, He-Xia Ni
In this paper, by constructing some identities, we prove some -analogues of some congruences. For example, for any odd integer , we show that \begin{gather*} \sum_{k=0}^{n-…
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…
Divisibility of some binomial sums
He-Xia Ni, Hao Pan
With help of -congruence, we prove the divisibility of some binomial sums. For example, for any integers , $$\sum_{k=0}^{n-1}(4k+1) \binom{2k}{k}^ρ\cdot (-4)^{ρ(n-1-k…
On the almost universality of
Hai-Liang Wu, He-Xia Ni, Hao Pan
In 2013, Farhi conjectured that for each , every natural number can be represented as with $x,y,z\in\Z…
Some symmetric -congruences
He-Xia Ni, Hao Pan
We prove some symmetric -congruences.