10 papers
Cyclic permutations of large subsets with polynomial values in multiplicative subgroups of finite fields
Hai-Liang Wu, He-Xia Ni
Let be a nonconstant polynomial with nonzero discriminant and let be an integer. For every sufficiently large prime , by applying m…
On the Burgess bound and Pythagorean triples involving primitive roots
Hai-Liang Wu, He-Xia Ni
By combining the recent results of Pierce and Xu on the higher-dimensional Burgess bound with the classical one-dimensional Burgess bound, we prove that for any sufficiently large…
On Diophantine -tuples related to primitive elements of finite fields
Hai-Liang Wu
Inspired by recent works on Diophantine tuples over finite fields, in this paper we consider Diophantine tuples related to primitive elements of finite fields. Let b…
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(Ï)=\left[G_N(Ï^{ki+ki})\right]_…
On -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 projective Fermat curve defined over a finite field, in this paper, we investigate some arithmetic properties of the cyc…
On restricted sums of four squares and Zhi-Wei Sun's conjecture
Hai-Liang Wu, Yue-Feng She
In 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 sa…