Chen Lin

activity

20242026

collaborators

9 papers

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…

math.CO2025

Kneser's theorem for codes and $ℓ$ -divisible set families

Chenying Lin, Gilles Zémor

A $k$ -wise $ℓ$ -divisible set family is a collection $F$ of subsets of ${1, \dots, n}$ such that any intersection of $k$ sets in $F$ has cardinality div…

math.NT2024

Galois orbits of torsion points over polytopes near atoral sets

Chenying Lin

Given an essentially atoral Laurent polynomial $P$ , we show an equidistribution theorem for the function $log ∣ P ∣$ on specific subsets of Galois orbits of torsion poi…

math.NT2024

The asymptotic estimation of prime ideals in imaginary quadratic fields and Chebyshev's bias

Chen Lin, Chenhao Tang, Xuejun Guo

We study the asymptotic estimation of prime ideals that satisfy certain congruence and argument conditions in imaginary quadratic fields. We also discuss the phenomenon of Chebyshe…

quant-ph2024

On the distillablity conjecture in matrix theory

Saiqi Liu, Chen Lin

The distillability conjecture of two-copy 4 by 4 Werner states is one of the main open problems in quantum information. We prove two special cases of the conjecture. The first case…

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

Kneser's theorem for codes and ℓ-divisible set families

Galois orbits of torsion points over polytopes near atoral sets

The asymptotic estimation of prime ideals in imaginary quadratic fields and Chebyshev's bias

On the distillablity conjecture in matrix theory

On the Fractional Parts of Polynomials Modulo $p$

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

Kneser's theorem for codes and $ℓ$ -divisible set families