Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Hai-liang Wu"'
Autor:
Hai-Liang Wu, Li-Yuan Wang
Publikováno v:
Electronic Research Archive, Vol 30, Iss 6, Pp 2109-2120 (2022)
Let $ p $ be an odd prime and let $ \mathbb{F}_p $ be the finite field of $ p $ elements. In 2019, Sun studied some permutations involving squares in $ \mathbb{F}_p $. In this paper, by the theory of local fields we generalize this topic to $ \mathbb
Externí odkaz:
https://doaj.org/article/13ee69b574ef411284115c23dcedc950
Publikováno v:
The Ramanujan Journal. 60:751-759
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a4430c3aac49d4f39d8c7be267d01167
https://doi.org/10.1007/s11139-022-00601-4
https://doi.org/10.1007/s11139-022-00601-4
Autor:
Hai-Liang Wu, Yue-Feng She
Publikováno v:
International Journal of Number Theory. 18:1749-1763
Let $p>3$ be a prime. Gauss first introduced the polynomial $S_p(x)=\prod_{c}(x-\zeta_p^c),$ where $0
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f3333ca7b51d9f7c4582fe95f8833614
https://doi.org/10.1142/s1793042122500890
https://doi.org/10.1142/s1793042122500890
Autor:
HAI-LIANG WU, LI-YUAN WANG
Publikováno v:
Bulletin of the Australian Mathematical Society. 106:243-253
We use circulant matrices and hyperelliptic curves over finite fields to study some arithmetic properties of certain determinants involving Legendre symbols and kth power residues.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c83f8f6ce057376e34b9a09714866ce1
https://doi.org/10.1017/s0004972722000053
https://doi.org/10.1017/s0004972722000053
Autor:
Li Yuan Wang, Hai Liang Wu
Publikováno v:
The Ramanujan Journal. 58:43-56
The evaluation of determinants with Legendre symbol entries is a classical topic both in number theory and in linear algebra. Recently Sun posed some conjectures on this topic. In this paper we confirm some of them via Gauss sums and the matrix deter
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5c7197964207f2c0965049049e98b2b7
https://doi.org/10.1007/s11139-021-00472-1
https://doi.org/10.1007/s11139-021-00472-1
Publikováno v:
Transactions of the American Mathematical Society. 374:7925-7944
In 2013, Farhi conjectured that for each $m\geq 3$, every natural number $n$ can be represented as $\lfloor x^2/m\rfloor+\lfloor y^2/m\rfloor+\lfloor z^2/m\rfloor$ with $x,y,z\in\Z$, where $\lfloor\cdot\rfloor$ denotes the floor function. Moreover, i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::834c5ef86f7f3f777ed40f56cc0b5b95
https://doi.org/10.1090/tran/8438
https://doi.org/10.1090/tran/8438
Autor:
Hai-Liang Wu, Zhi-Wei Sun
Publikováno v:
Acta Arithmetica. 193:253-268
The 1-3-5 conjecture of Z.-W. Sun states that any $n\in\mathbb N=\{0,1,2,\ldots\}$ can be written as $x^2+y^2+z^2+w^2$ with $w,x,y,z\in\mathbb N$ such that $x+3y+5z$ is a square. In this paper, via the theory of ternary quadratic forms and related mo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::24318de26b684875109298867d199392
https://doi.org/10.4064/aa180911-9-8
https://doi.org/10.4064/aa180911-9-8
Autor:
Hai Liang Wu, Li Yuan Wang
Publikováno v:
Bulletin of the Australian Mathematical Society. 100:362-371
Let $n$ be a positive integer and $a$ an integer prime to $n$. Multiplication by $a$ induces a permutation over $\mathbb{Z}/n\mathbb{Z}=\{\overline{0},\overline{1},\ldots ,\overline{n-1}\}$. Lerch’s theorem gives the sign of this permutation. We ex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9d6780cb6951e7d0a57c4301d1116cff
https://doi.org/10.1017/s000497271900073x
https://doi.org/10.1017/s000497271900073x
Autor:
HAI-LIANG WU, YUE-FENG SHE
Let $p=3n+1$ be a prime with $n\in\mathbb{N}=\{0,1,\cdots\}$, and let $g\in\mathbb{Z}$ be a primitive root modulo $p$. Let $0
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43fed26b4431af9af2db7581cb67316d
http://arxiv.org/abs/2105.09822
http://arxiv.org/abs/2105.09822
Let $��_{n}(q)$ 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 integer $n>1$, \begin{align*} &\sum_{k=0}^{n-1}[8k-1]\frac{(q^{-1};
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d02e7db489f76a55bcb249f97fa14424