Kaimin Cheng

activity

20242026

collaborators

8 papers

math.NT2026

On the $2$ -adic valuation of $σ_{k} (n)$

Kaimin Cheng, Ke Zhang

For a positive integer $k$ , let \[ σ_k(n)=\sum_{d\mid n} d^k \] be the divisor function of order $k$ , and let $ν_{p} (m)$ denote the $p$ -adic valuation of an integer $m$ . Motivated by…

math.NT2025

The $3$ -sparsity of $X^{n} - 1$ over finite fields

Kaimin Cheng

Let $q$ be a prime power and $F_{q}$ the finite field with $q$ elements. For a positive integer $n$ , the binomial $X^{n} - 1 \in F_{q} [X]$ is said to be $3$ -sparse over…

math.NT2025

The $3$ -sparsity of $X^{n} - 1$ over finite fields, II

Kaimin Cheng

Let $q$ be a power of $2$ and let $F_{q}$ be the finite field with $q$ elements. For a positive integer $n$ , the polynomial $X^{n} - 1 \in F_{q} [X]$ is called $3$ -sparse ov…

cs.CR2025

Weight distribution of a class of $p$ -ary codes

Kaimin Cheng, Du Sheng

Let $p$ be a prime, and let $N$ be a positive integer such that $p$ is a primitive root modulo $N$ . Define $q = p^{e}$ , where $e = ϕ (N)$ , and let $F_{q}$ be the finite field o…

math.NT2025

Multiplicative character sums over two classes of subsets of quadratic extensions of finite fields

Kaimin Cheng, Arne Winterhof

Let $q$ be a prime power and $r$ a positive even integer. Let $F_{q}$ be the finite field with $q$ elements and $F_{q^{r}}$ be its extension field of degree $r$ . Le…

math.NT2024

The inverse stability of Artin-Schreier polynomials over finite fields

Kaimin Cheng

Let $p$ be a prime number and $q$ a power of $p$ . Let $F_{q}$ be the finite field with $q$ elements. For a positive integer $n$ and a polynomial $φ (X) \in F_{q} [X]$ , le…

On the 2-adic valuation of σk​(n)

The 3-sparsity of Xn−1 over finite fields

The 3-sparsity of Xn−1 over finite fields, II

Weight distribution of a class of p-ary codes

Multiplicative character sums over two classes of subsets of quadratic extensions of finite fields

The inverse stability of Artin-Schreier polynomials over finite fields

On the $2$ -adic valuation of $σ_{k} (n)$

The $3$ -sparsity of $X^{n} - 1$ over finite fields

The $3$ -sparsity of $X^{n} - 1$ over finite fields, II

Weight distribution of a class of $p$ -ary codes