Li-Yuan Wang

activity

20182026

most citedApplications of Lerch's theorem and permutations concerning quadratic residues

3 citations · 10 across the 18 of their papers we have counts for

collaborators

18 papers

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.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

On a determinant involving linear combinations of Legendre symbols

Keqin Liu, Zhi-Wei Sun, Li-Yuan Wang

In this paper, we prove a conjecture of the second author by evaluating the determinant $$\det\left[x + \left(\frac{i-j}p\right) + \left(\frac ip\right)y + \left(\frac jp\right)z +…

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

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.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

Frobenius matrices and a variant of Zolotarev's theorem

Hai-Liang Wu, Li-Yuan Wang

In this paper, with the help of the theory of matrices and finite fields we generalize Zolotarev's theorem to an arbitrary finite dimensional vector space over $F_{q}$ , wher…

math.NT2020★ 2 cited

Two $q$ -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 $q$ -supercongruences in a unified way. In this paper, we app…

math.NT2020

Products of quadratic residues and related identities

Hai-Liang Wu, Li-Yuan Wang

In this paper we study products of quadratic residues modulo odd primes and prove some identities involving quadratic residues. For instance, let $p$ be an odd prime. We prove that…

math.NT2018★ 3 cited

Applications of Lerch's theorem and permutations concerning quadratic residues

Li-Yuan Wang, Hai-Liang Wu

Let $p$ be an odd prime. For each integer $a$ with $p ∤ a$ , the famous Zolotarev's Lemma says that the Legendre symbol $(\frac{a}{p})$ is the sign of the permutation of $Z / p Z$ …

math.NT2018★ 3 cited

On practical numbers of some special forms

Li-Yuan Wang, Zhi-Wei Sun

In this paper we study practical numbers of some special forms. For any integers $b \geq 0$ and $c > 0$ , we show that if $n^{2} + bn + c$ is practical for some integer $n > 1$ , then there are i…

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

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

On a determinant involving linear combinations of Legendre symbols

Gaussian hypergeometric functions and cyclotomic matrices

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

Cyclotomic matrices and hypergeometric functions over finite fields

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

q-Supercongruences from transformation formulas

Frobenius matrices and a variant of Zolotarev's theorem

Two q-supercongruences from Watson's transformation

Products of quadratic residues and related identities

Applications of Lerch's theorem and permutations concerning quadratic residues

On practical numbers of some special forms

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 $det M_{p}$

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

$q$ -Supercongruences from transformation formulas

Two $q$ -supercongruences from Watson's transformation