Hai-Liang Wu

activity

20162026

most citedThe supersingular locus of unitary Shimura varieties with exotic good reduction

13 citations · 26 across the 46 of their papers we have counts for

collaborators

46 papers

math.NT2026

Cyclic permutations of large subsets with polynomial values in multiplicative subgroups of finite fields

Hai-Liang Wu, He-Xia Ni

Let $f (t) \in Z [t]$ be a nonconstant polynomial with nonzero discriminant and let $k \geq 2$ be an integer. Inspired by the work of Alon and Bourgain, for sufficiently large pr…

math.NT2026

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…

math.NT2026

On Diophantine $m$ -tuples related to primitive elements of finite fields

Hai-Liang Wu

Inspired by recent works on Diophantine tuples over finite fields, in this paper we consider Diophantine tuples related to primitive elements of finite fields. Let $F_{q}$ b…

math.NT2026

The Gauss periods and cyclotomic matrices involving Gauss sums over cyclic groups

Hai-Liang Wu, Li-Yuan Wang

In this paper, by using the arithmetic properties of the Gauss periods and character sums over cyclic groups, we study the cyclotomic matrix $$A_k(χ)=\left[G_N(χ^{ki+ki})\right]_{0…

math.NT2026

Products involving the real parts of Jacobi sums and related cyclotomic matrices

Hai-Liang Wu, Xiao-Han Ji

Let $q$ be an odd prime power and $χ_{q}$ be a generator of the group of all multiplicative characters of $F_{q}$ . In this paper, we study the arithmetic properties of the pro…

math.NT2025

On restricted sums of four squares and Zhi-Wei Sun's $x + 24 y$ conjecture

Hai-Liang Wu, Yue-Feng She

In this paper, by using the arithmetic theory of ternary quadratic forms, we study some refinements on Lagrange's four-square theorem. For example, given positive integers $a, b$ sa…

math.NT2025

On $p$ -th cyclotomic field and cyclotomic matrices involving Jacobi sums

Hai-Liang Wu, Li-Yuan Wang, Hao Pan

Inspired by Weil's classical result on the zeta function of a projective Fermat curve defined over a finite field, in this paper, we investigate some arithmetic properties of the c…

math.NT2025

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 $p$ -adic tools, we study certain cyclotomic matrices involving squares over finite fields. For example, l…

math.NT2024

The Gross-Koblitz formula and almost circulant matrices related to Jacobi sums

Hai-Liang Wu, Li-Yuan Wang

In this paper, we mainly consider arithmetic properties of the cyclotomic matrix $B_{p} (k) = [J_{p} (χ^{k i}, χ^{k j})^{- 1}]_{1 \leq i, j \leq (p - 1 - k) / k}$ , where $p$ is an odd prime, $…

math.NT2024

Gaussian hypergeometric functions and cyclotomic matrices

Hai-Liang Wu, Li-Yuan Wang

Let $q = p^{n}$ be an odd prime power and let $F_{q}$ be the finite field with $q$ elements. Let $F_{q}^{\times}$ be the group of all multiplicative characters…

math.NT2024★ 1 cited

A conjecture of Zhi-Wei Sun on matrices concerning multiplicative subgroups of finite fields

Jie Li, Hai-Liang Wu

Motivated by the recent work of Zhi-Wei Sun on determinants involving the Legendre symbol, in this paper, we study some matrices concerning subgroups of finite fields. For example,…

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.NT2024★ 1 cited

On cyclotomic matrices involving Gauss sums over finite fields

Hai-Liang Wu, Jie Li, Li-Yuan Wang +1

Inspired by the works of L. Carlitz and Z.-W. Sun on cyclotomic matrices, in this paper, we investigate certain cyclotomic matrices involving Gauss sums over finite fields, which c…

math.NT2024

On the cyclotomic field $Q (e^{2 π i / p})$ and Zhi-Wei Sun's conjecture on $det M_{p}$

Li-Yuan Wang, Hai-Liang Wu

In 2019, Zhi-Wei Sun posed an interesting conjecture on certain determinants with Legendre symbol entries. In this paper, by using the arithmetic properties of $p$ -th cyclotomic fi…

math.NT2023

On finite field analogues of determinants involving the Beta function

Hai-Liang Wu, Li-Yuan Wang, Hao Pan

Motivated by the works of L. Carlitz, R. Chapman and Z.-W. Sun on cyclotomic matrices, in this paper, we investigate certain cyclotomic matrices concerning the Jacobi sums over fin…

math.NT2023

On generalized Legendre matrices involving roots of unity over finite fields

Ning-Liu Wei, Yu-Bo Li, Hai-Liang Wu

In this paper, motivated by the work of Chapman, Vsemirnov and Sun et al., we investigate some arithmetic properties of the generalized Legendre matrices over finite fields. For ex…

math.NT2023★ 2 cited

On sumsets involving $k$ th powers of finite fields

Hai-Liang Wu, Ning-Liu Wei, Yu-Bo Li

In this paper, we study some topics concerning the additive decompositions of the set $D_{k}$ of all $k$ th power residues modulo a prime $p$ . For example, given a positive integer $k…

math.NT2022

Trinomial coefficients and related matrices over finite fields

Yue-Feng She, Hai-Liang Wu

In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields…

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.NT2022

On additive decompositions of primitive elements in finite fields

Hai-Liang Wu, Yue-Feng She

In this paper, we study several topics on additive decompositions of primitive elemements in finite fields. Also we refine some bounds obtained by Dartyge and Sárközy and Shparlins…

math.NT2021★ 1 cited

Cyclotomic matrices and hypergeometric functions over finite fields

Hai-Liang Wu, Yue-Feng She, Li-Yuan Wang

With the help of hypergeometric functions over finite fields, we study some arithmetic properties of cyclotomic matrices involving characters and binary quadratic forms over finite…

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

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 $F_{q}$ be the finite field of $q$ elements and let $a_{1}, a_{2}, \dots, a_{q - 1}$ be all nonzero elements of…

Cyclic permutations of large subsets with polynomial values in multiplicative subgroups of finite fields

On the Burgess bound and Pythagorean triples involving primitive roots

On Diophantine m-tuples related to primitive elements of finite fields

The Gauss periods and cyclotomic matrices involving Gauss sums over cyclic groups

Products involving the real parts of Jacobi sums and related cyclotomic matrices

On restricted sums of four squares and Zhi-Wei Sun's x+24y conjecture

On p-th cyclotomic field and cyclotomic matrices involving Jacobi sums

The Pell sequence and cyclotomic matrices involving squares over finite fields

The Gross-Koblitz formula and almost circulant matrices related to Jacobi sums

Gaussian hypergeometric functions and cyclotomic matrices

A conjecture of Zhi-Wei Sun on matrices concerning multiplicative subgroups of finite fields

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

On cyclotomic matrices involving Gauss sums over finite fields

On the cyclotomic field Q(e2πi/p) and Zhi-Wei Sun's conjecture on detMp​

On finite field analogues of determinants involving the Beta function

On generalized Legendre matrices involving roots of unity over finite fields

On sumsets involving kth powers of finite fields

Trinomial coefficients and related matrices over finite fields

Additive decompositions of cubes in finite fields

On additive decompositions of primitive elements in finite fields

Cyclotomic matrices and hypergeometric functions over finite fields

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

q-Supercongruences from transformation formulas

A conjecture of Zhi-Wei Sun on determinants over finite fields

On Diophantine $m$ -tuples related to primitive elements of finite fields

On restricted sums of four squares and Zhi-Wei Sun's $x + 24 y$ conjecture

On $p$ -th cyclotomic field and cyclotomic matrices involving Jacobi sums

On the cyclotomic field $Q (e^{2 π i / p})$ and Zhi-Wei Sun's conjecture on $det M_{p}$

On sumsets involving $k$ th powers of finite fields

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

$q$ -Supercongruences from transformation formulas