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math.NT2025
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…
math.NT2025
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 a projective Fermat curve defined over a finite field, in this paper, we investigate some arithmetic properties of the c…
math.NT2025
The Pell sequence and cyclotomic matrices involving squares over finite fields
Hai-Liang Wu, Li-Yuan Wang, He-Xia Ni
In this paper, by some arithmetic properties of the Pell sequence and some -adic tools, we study certain cyclotomic matrices involving squares over finite fields. For example, l…