HWHai-Liang Wu
Hai-Liang Wu
*This is an algorithmically generated author record based on publicly available information.
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Hai-Liang Wu has a total of 14 co-authors. Here are the top co-authors by number of shared publications:
- Li-Yuan Wang
School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing, People’s Republic of China
18 shared publications - Yue-Feng She
Department of Mathematics, Nanjing University, Nanjing, People’s Republic of China
13 shared publications - He-Xia Ni
Department of Applied Mathematics, Nanjing Audit University, Nanjing, People’s Republic of China
6 shared publications - Zhi-Wei Sun
School of Mathematics, Nanjing University, Nanjing 210093, China
6 shared publications - Ning-Liu Wei
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu Province, PR China
4 shared publications - Yu-Bo Li
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu Province, PR China
4 shared publications
Latest Publications
- 29 October 2026
- Published by Elsevier in Finite Fields and Their Applications
- Vol. 119
On p-th cyclotomic field and cyclotomic matrices involving Jacobi sums
- 29 October 2026
- Published by Elsevier in Finite Fields and Their Applications
- Vol. 119
On p-th cyclotomic field and cyclotomic matrices involving Jacobi sums
- 12 February 2026
- Published by Springer Nature in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
- Vol. 120 (2) , 43
On a generalization of R. Chapman’s “evil determinant”
- 12 February 2026
- Published by Springer Nature in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
- Vol. 120 (2) , 43
On a generalization of R. Chapman’s “evil determinant”
- Open AccessOn restricted sums of four squares and Zhi-Wei Sun's $x+24y$ conjectureIn 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 $a,b$ satisfying some algebraic conditions and a positive integer $C\ge3$, we will show that for any sufficiently large integer $n$ with $\ord_2(n)\le C$, there exist non-negative integers $x,y,z,w$ such that $$ \begin{cases} x^2+y^2+z^2+w^2=n, ax+by\in\mathcal{S}, \end{cases} $$ where $\mathcal{S}$ is the set of all squares over $\mathbb{Z}$. In particular, we obtain some progress on Zhi-Wei Sun's $x+24y$ conjecture.Open AccessOn restricted sums of four squares and Zhi-Wei Sun's $x+24y$ conjectureIn 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 $a,b$ satisfying some algebraic conditions and a positive integer $C\ge3$, we will show that for any sufficiently large integer $n$ with $\ord_2(n)\le C$, there exist non-negative integers $x,y,z,w$ such that $$ \begin{cases} x^2+y^2+z^2+w^2=n, ax+by\in\mathcal{S}, \end{cases} $$ where $\mathcal{S}$ is the set of all squares over $\mathbb{Z}$. In particular, we obtain some progress on Zhi-Wei Sun's $x+24y$ conjecture.
- Open Access
- 13 November 2025
- Published by Institute of Mathematics, Polish Academy of Sciences in Acta Arithmetica
- p. 1-17
On finite field analogues of determinants involving the Beta function
Motivated by the works of L. Carlitz, R. Chapman and Z.-W. Sun on cyclotomic matrices, we investigate certain cyclotomic matrices concerning Jacobi sums over finite fields, which can be viewed as finite field analogues of certain matrices involving the Beta function. For example, let q>1 be a prime power and let χ be a generator of the group of all multiplicative characters of Fq. Then we prove that det[Jq(χi,χj)]1≤i,j≤q−2=(q−1)q−3, where Jq(χi,χj) is the Jacobi sum over Fq. This is a finite analogue of det[B(i,j)]1≤i,j≤n=(−1)n(n−1)/2∏r=0n−1(r!)3(n+r)!, where B is the Beta function. Also, if q=p≥5 is an odd prime, then we show that det[Jp(χ2i,χ2j)]1≤i,j≤(p−3)/2=1+(−1)(p+1)/2p4(p−12)(p−5)/2.
- 13 November 2025
- Published by Institute of Mathematics, Polish Academy of Sciences in Acta Arithmetica
- p. 1-17
Open AccessOn finite field analogues of determinants involving the Beta function
Motivated by the works of L. Carlitz, R. Chapman and Z.-W. Sun on cyclotomic matrices, we investigate certain cyclotomic matrices concerning Jacobi sums over finite fields, which can be viewed as finite field analogues of certain matrices involving the Beta function. For example, let q>1 be a prime power and let χ be a generator of the group of all multiplicative characters of Fq. Then we prove that det[Jq(χi,χj)]1≤i,j≤q−2=(q−1)q−3, where Jq(χi,χj) is the Jacobi sum over Fq. This is a finite analogue of det[B(i,j)]1≤i,j≤n=(−1)n(n−1)/2∏r=0n−1(r!)3(n+r)!, where B is the Beta function. Also, if q=p≥5 is an odd prime, then we show that det[Jp(χ2i,χ2j)]1≤i,j≤(p−3)/2=1+(−1)(p+1)/2p4(p−12)(p−5)/2.
- 10 February 2025
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 153 (4) , 1411-1424
On cyclotomic matrices involving Gauss sums over finite fields
Inspired by the works of L. Carlitz [Acta Arith. 5 (1959), pp. 293–308] and Z.-W. Sun [Finite Fields Appl. 56 (2019), pp. 285–307] on cyclotomic matrices, in this paper, we investigate certain cyclotomic matrices involving Gauss sums over finite fields, which can be viewed as finite field analogues of certain matrices related to the Gamma function. For example, letbe an odd prime power with prime and . Let and let be a generator of the group of all multiplicative characters of the finite field . For the Gauss sum we prove that where - 10 February 2025
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 153 (4) , 1411-1424
On cyclotomic matrices involving Gauss sums over finite fields
Inspired by the works of L. Carlitz [Acta Arith. 5 (1959), pp. 293–308] and Z.-W. Sun [Finite Fields Appl. 56 (2019), pp. 285–307] on cyclotomic matrices, in this paper, we investigate certain cyclotomic matrices involving Gauss sums over finite fields, which can be viewed as finite field analogues of certain matrices related to the Gamma function. For example, letbe an odd prime power with prime and . Let and let be a generator of the group of all multiplicative characters of the finite field . For the Gauss sum we prove that where - 21 January 2025
- Published by Elsevier in Finite Fields and Their Applications
- Vol. 103
The Gross-Koblitz formula and almost circulant matrices related to Jacobi sums
- 21 January 2025
- Published by Elsevier in Finite Fields and Their Applications
- Vol. 103
The Gross-Koblitz formula and almost circulant matrices related to Jacobi sums
- 1 November 2024
- Published by Elsevier in Finite Fields and Their Applications
- Vol. 101
On the cyclotomic field and Zhi-Wei Sun's conjecture on det M- 1 November 2024
- Published by Elsevier in Finite Fields and Their Applications
- Vol. 101
On the cyclotomic field and Zhi-Wei Sun's conjecture on det M- Open Access
- 27 September 2024
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 111 (3) , 490-496
A CONJECTURE OF ZHI-WEI SUN ON MATRICES CONCERNING MULTIPLICATIVE SUBGROUPS OF FINITE FIELDS
Motivated by the recent work of Zhi-Wei Sun [‘Problems and results on determinants involving Legendre symbols’, Preprint, arXiv:2405.03626], we study some matrices concerning subgroups of finite fields. For example, let $q\equiv 3\pmod 4$ be an odd prime power and let $\phi $ be the unique quadratic multiplicative character of the finite field $\mathbb {F}_q$ . If the set $\{s_1,\ldots ,s_{(q-1)/2}\}=\{x^2:\ x\in \mathbb {F}_q\setminus \{0\}\}$ , then we prove that $$ \begin{align*}\det[t+\phi(s_i+s_j)+\phi(s_i-s_j)]_{1\le i,j\le (q-1)/2}=\bigg(\frac{q-1}{2}t-1\bigg)q^{{(q-3)}/{4}}.\end{align*} $$ This confirms a conjecture of Zhi-Wei Sun.- 27 September 2024
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 111 (3) , 490-496
Open AccessA CONJECTURE OF ZHI-WEI SUN ON MATRICES CONCERNING MULTIPLICATIVE SUBGROUPS OF FINITE FIELDS
Motivated by the recent work of Zhi-Wei Sun [‘Problems and results on determinants involving Legendre symbols’, Preprint, arXiv:2405.03626], we study some matrices concerning subgroups of finite fields. For example, let $q\equiv 3\pmod 4$ be an odd prime power and let $\phi $ be the unique quadratic multiplicative character of the finite field $\mathbb {F}_q$ . If the set $\{s_1,\ldots ,s_{(q-1)/2}\}=\{x^2:\ x\in \mathbb {F}_q\setminus \{0\}\}$ , then we prove that $$ \begin{align*}\det[t+\phi(s_i+s_j)+\phi(s_i-s_j)]_{1\le i,j\le (q-1)/2}=\bigg(\frac{q-1}{2}t-1\bigg)q^{{(q-3)}/{4}}.\end{align*} $$ This confirms a conjecture of Zhi-Wei Sun. - Open Access
On a generalization of R. Chapman's "evil determinant"
Let $p$ be an odd prime and $x$ be an indeterminate. Recently, Z.-W. Sun proposed the following conjecture: $$\det\left[x+\left(\frac{j-i}{p}\right)\right]_{0\le i,j\le \frac{p-1}{2}}=\begin{cases} (\frac{2}{p})pb_px-a_p & \mbox{if}\ p\equiv 1\pmod4, 1 & \mbox{if}\ p\equiv 3\pmod4, \end{cases}$$ where $a_p$ and $b_p$ are rational numbers related to the fundamental unit and class number of the real quadratic field $\mathbb{Q}(\sqrt{p})$. In this paper, we confirm the above conjecture of Sun based on Vsemirnov's decomposition of Chapman's "evil determinant".Open AccessOn a generalization of R. Chapman's "evil determinant"
Let $p$ be an odd prime and $x$ be an indeterminate. Recently, Z.-W. Sun proposed the following conjecture: $$\det\left[x+\left(\frac{j-i}{p}\right)\right]_{0\le i,j\le \frac{p-1}{2}}=\begin{cases} (\frac{2}{p})pb_px-a_p & \mbox{if}\ p\equiv 1\pmod4, 1 & \mbox{if}\ p\equiv 3\pmod4, \end{cases}$$ where $a_p$ and $b_p$ are rational numbers related to the fundamental unit and class number of the real quadratic field $\mathbb{Q}(\sqrt{p})$. In this paper, we confirm the above conjecture of Sun based on Vsemirnov's decomposition of Chapman's "evil determinant". - Open Access
On cyclotomic matrices involving Gauss sums over finite fields
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 can be viewed as finite field analogues of certain matrices related to the Gamma function. For example, let $q=p^n$ be an odd prime power with $p$ prime and $n\in\mathbb{Z}^+$. Let $ζ_p=e^{2π{\bf i}/p}$ and let $χ$ be a generator of the group of all mutiplicative characters of the finite field $\mathbb{F}_q$. For the Gauss sum $$G_q(χ^{r})=\sum_{x\in\mathbb{F}_q}χ^{r}(x)ζ_p^{{\rm Tr}_{\mathbb{F}_q/\mathbb{F}_p}(x)},$$ we prove that $$\det \left[G_q(χ^{2i+2j})\right]_{0\le i,j\le (q-3)/2}=(-1)^{α_p}\left(\frac{q-1}{2}\right)^{\frac{q-1}{2}}2^{\frac{p^{n-1}-1}{2}},$$ where $$α_p= \begin{cases} 1 & \mbox{if}\ n\equiv 1\pmod 2, (p^2+7)/8 & \mbox{if}\ n\equiv 0\pmod 2. \end{cases}$$Open AccessOn cyclotomic matrices involving Gauss sums over finite fields
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 can be viewed as finite field analogues of certain matrices related to the Gamma function. For example, let $q=p^n$ be an odd prime power with $p$ prime and $n\in\mathbb{Z}^+$. Let $ζ_p=e^{2π{\bf i}/p}$ and let $χ$ be a generator of the group of all mutiplicative characters of the finite field $\mathbb{F}_q$. For the Gauss sum $$G_q(χ^{r})=\sum_{x\in\mathbb{F}_q}χ^{r}(x)ζ_p^{{\rm Tr}_{\mathbb{F}_q/\mathbb{F}_p}(x)},$$ we prove that $$\det \left[G_q(χ^{2i+2j})\right]_{0\le i,j\le (q-3)/2}=(-1)^{α_p}\left(\frac{q-1}{2}\right)^{\frac{q-1}{2}}2^{\frac{p^{n-1}-1}{2}},$$ where $$α_p= \begin{cases} 1 & \mbox{if}\ n\equiv 1\pmod 2, (p^2+7)/8 & \mbox{if}\ n\equiv 0\pmod 2. \end{cases}$$