15 citations · 20 across the 24 of their papers we have counts for
8 papers · 1 filter
On determinants involving
Deyi Chen, Zhi-Wei Sun
Let be an odd prime. In this paper, we mainly evaluate determinants involving , where denotes the Legendre symbol. When $…
On determinants involving and
Deyi Chen, Zhi-Wei Sun
Let be an odd prime and let be the Legendre symbol. In this paper, we study the determinant $$\det\left[\left(\frac{j^2-k^2}p\right)+\left(\frac{jk}p\right)w\…
On a determinant involving linear combinations of Legendre symbols
Keqin Liu, Zhi-Wei Sun, Li-Yuan Wang
In this paper, we prove a conjecture of the second author by evaluating the determinant $$\det\left[x + \left(\frac{i-j}p\right) + \left(\frac ip\right)y + \left(\frac jp\right)z +…
Some determinants involving binary forms
Yue-Feng She, Zhi-Wei Sun
In this paper, we study arithmetic properties of certain determinants involving powers of , where and are integers. For example, for any odd integer wit…
Problems and results on determinants involving Legendre symbols
Zhi-Wei Sun
In this paper we investigate determinants whose entries are linear combinations of Legendre symbols. We deduce some new results in this direction; for example, we prove that for an…
On some determinants arising from quadratic residues
Chen-Kai Ren, Zhi-Wei Sun
Let be a prime, and let with . For the determinants $$S_m(d,p)=\det\left[(i^2+dj^2)^{m}\right]_{1\leqslant i,j \leqslant (p-1)/2}\ \ \left(\frac{p-1…
Proof of conjectures on series with summands involving
Zhi-Wei Sun, Yajun Zhou
Using cyclotomic multiple zeta values of level , we confirm and generalize several conjectural identities on infinite series with summands involving $\binom{2k}k8^k/(\binom{3k}k…
Evaluations of and related series
Zhi-Wei Sun, Yajun Zhou
We perform polylogarithmic reductions for several classes of infinite sums motivated by Z.-W. Sun's related works in 2022--2023. For certain choices of parameters, these series can…