Chen Lin

activity

20242026

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5 papers · 1 filter

math.RA2026

Generic Nullity of Generalized Commutators

Chen Lin, Chenhao Tang, Enhan Zhao

We study the generic nullity of generalized commutator operators \[L_{\mathbf{A}}(X)=s_{k+1}(A_1,\cdots,A_k,X)\] on matrix algebras, where $s_{k + 1}$ denotes the standard polynomial…

math.NT2026

On the Fractional Parts of Polynomials Modulo $p$

Xuejun Guo, Chen Lin, Zhefeng Xu

We study a half-interval distribution problem for polynomial residues modulo an odd prime $p$ : how often the fractional part of $φ (x) / p$ lies in the upper half of the unit interval…

math.NT2026

The $p$ -rationality of $Q (- (k p + m))$ and $Q (p (p + 1))$

Chen Lin, Xuejun Guo

In this paper, we construct new families of imaginary and real quadratic fields that are $p$ -rational. In the imaginary case, we prove that for any positive integer $k$ and any int…

math.NT2026

Matrix Kloosterman sums and product-trace estimates for semisimple algebras

Xuejun Guo, Chen Lin, Chenhao Tang

Let $k = F_{q}$ , $E = F_{q^{n}}$ and $Tr = Tr_{E / k}$ . For $r \geq 2$ , $a \in k^{\times}$ and $x \in E^{\times}$ , let $N (E, r, x, a)$ be the number of $r…

math.NT2026

Counting Polynomial-type Exceptional Units on Algebraic Varieties over Number Fields

Chen Lin, Kaihan Tang

Previous research on exceptional units has primarily focused on the ring of rational integers or abstract finite rings, often restricted to linear or quadratic constraints. In this…

Generic Nullity of Generalized Commutators

On the Fractional Parts of Polynomials Modulo p

The p-rationality of Q(−(kp+m)​) and Q(p(p+1)​)

Matrix Kloosterman sums and product-trace estimates for semisimple algebras

Counting Polynomial-type Exceptional Units on Algebraic Varieties over Number Fields

On the Fractional Parts of Polynomials Modulo $p$

The $p$ -rationality of $Q (- (k p + m))$ and $Q (p (p + 1))$