Hai-Liang Wu

activity

20182024

collaborators

16 papers

math.NT2024

On a generalization of R. Chapman's "evil determinant"

Li-Yuan Wang, Hai-Liang Wu, He-Xia Ni

Let $p$ be an odd prime and $x$ 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}{…

math.NT2022

Additive decompositions of cubes in finite fields

Hai-Liang Wu, Yue-Feng She

Let $p \equiv 1 (mod 3)$ be a prime . We study several topics on additive decompositions concerning the set $C_{p}$ of all non-zero cubes in the finite field of $p$ elements. For example…

math.NT2021

Applications of circulant matrices to determinants involving $k$ -th power residues

Hai-Liang Wu, Li-Yuan Wang

In this paper, by the tools of circulant matrices and hyperelliptic curves over finite fields, we study some arithmetic properties of certain determinants involving the Legendre sy…

math.NT2021

$q$ -Supercongruences from transformation formulas

He-Xia Ni, Li-Yuan Wang, Hai-Liang Wu

Let $Φ_{n} (q)$ denote the $n$ -th cyclotomic polynomial in $q$ . Recently, Guo and Schlosser [Constr. Approx. 53 (2021), 155--200] put forward the following conjecture: for an odd in…

math.NT2021

Cubes in finite fields and related permutations

Hai-Liang Wu, Yue-Feng She

Let $p = 3 n + 1$ be a prime with $n \in N = {0, 1, \dots}$ , and let $g \in Z$ be a primitive root modulo $p$ . Let $0 < a_{1} < \dots < a_{n} < p$ be all the cubic residues modulo $p$ …

math.NT2021

Primitive elements and $k$ -th powers in finite fields

Hai-Liang Wu, Yue-Feng She

Let $F_{q}$ be the finite field of $q$ elements, and let $k ∣ q - 1$ be a positive integer. Let $f (x) = a x^{2} + b x + c$ be a quadratic polynomial in $F_{q} [x]$ with $b^2-4ac…

On a generalization of R. Chapman's "evil determinant"

Additive decompositions of cubes in finite fields

Applications of circulant matrices to determinants involving k-th power residues

q-Supercongruences from transformation formulas

Cubes in finite fields and related permutations

Primitive elements and k-th powers in finite fields

Applications of circulant matrices to determinants involving $k$ -th power residues

$q$ -Supercongruences from transformation formulas

Primitive elements and $k$ -th powers in finite fields