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pro vyhledávání: '"WANG, Li Yuan"'
Autor:
Wu, Hai-Liang, Wang, Li-Yuan
In this paper, we mainly consider the arithmetic properties of the cyclotomic matrix $B_p(k)=\left[J_p(\chi^{ki},\chi^{kj})^{-1}\right]_{1\le i,j\le (p-1-k)/k}$, where $p$ is an odd prime, $1\le k
Externí odkaz:
http://arxiv.org/abs/2409.13307
In this paper, we prove a conjecture of the second author by evaluating the determinant $$\det\left[x+\left(\frac{i-j}p\right)+\left(\frac ip\right)y+\left(\frac jp\right)z+\left(\frac{ij}p\right)w\right]_{0\le i,j\le(p-3)/2}$$ for any odd prime $p$,
Externí odkaz:
http://arxiv.org/abs/2408.07034
Autor:
Wu, Hai-Liang, Wang, Li-Yuan
Let $q=p^n$ be an odd prime power and let $\mathbb{F}_q$ be the finite field with $q$ elements. Let $\widehat{\mathbb{F}_q^{\times}}$ be the group of all multiplicative characters of $\mathbb{F}_q$ and let $\chi$ be a generator of $\widehat{\mathbb{F
Externí odkaz:
http://arxiv.org/abs/2407.20583
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,
Externí odkaz:
http://arxiv.org/abs/2405.02112
Publikováno v:
Proc. Amer. Math. Soc., 2024
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
Externí odkaz:
http://arxiv.org/abs/2404.15063
Autor:
Wang, Li-Yuan, Wu, Hai-Liang
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 field and the finite field $\mathbb{F}_p$, we confirm this conjecture.
Externí odkaz:
http://arxiv.org/abs/2401.05853
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 finite fields, which can be viewed as finite field analogues of certain m
Externí odkaz:
http://arxiv.org/abs/2307.12261
Let $\mathcal{S}=\{1^2,2^2,3^2,...\}$ be the set of squares and $\mathcal{W}=\{w_n\}_{n=1}^{\infty} \subset \mathbb{N}$ be an additive complement of $\mathcal{S}$ so that $\mathcal{S} + \mathcal{W} \supset \{n \in \mathbb{N}: n \geq N_0\}$ for some $
Externí odkaz:
http://arxiv.org/abs/2211.16810
Autor:
Wang, Li-Yuan, Wu, Hai-Liang
Publikováno v:
In Finite Fields and Their Applications January 2025 101
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 fields. Also, we confirm some related conjectures posed by Zhi-Wei Su
Externí odkaz:
http://arxiv.org/abs/2111.01661