Kaimin Cheng

collaborators

10 papers

math.NT2026

The complete cubic Walsh spectrum of a permutation-inverse Boolean family

Kaimin Cheng

Let $q = 2^{e}$ with $e \geq 2$ even, put $d = (q^{2} + q + 1) /3$ , and let $I ¨ (X) = X + X^{d} + X^{d q}$ be the permutation of $F_{q^{2}}$ introduced by Ding, Qu, Wang, Yuan, and Yuan. For $Î±\in\ma…

math.NT2026

A first-exit proof of Cusick's sum-of-digits conjecture

Kaimin Cheng

We prove Cusick's conjecture on the binary sum-of-digits function. More precisely, for every integer $t\ge 1$ we show that \[ c_t:=\lim_{N\to\infty}\frac{1}{N} \#\{0\le n<N:\ s_2…

math.NT2026

A proof of a permutation-inverse bent-function conjecture

Kaimin Cheng

Let $q = 2^{e}$ with $e$ even, and let $F_{q^{2}}$ be the finite field of order $q^{2}$ . Put $d = (q^{2} + q + 1) /3$ , and consider the permutation polynomial $$ Ï(X)=X+X^d+X^{dq}\in\mathb…

math.NT2026

Banded quadratic digit functions along irreducible polynomials over finite fields

Kaimin Cheng

Let $q$ be an odd prime power and let $\F_q$ be the finite field with $q$ elements. Let $P (n)$ be the set of monic irreducible polynomials of degree $n$ over $\mathbb{F}_…

math.NT2026

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…

math.NT2026

On the $2$ -adic valuation of $I ¨ _{k} (n)$

Kaimin Cheng, Ke Zhang

For a positive integer $k$ , let \[ Ï_k(n)=\sum_{d\mid n} d^k \] be the divisor function of order $k$ , and let $I^½_{p} (m)$ denote the $p$ -adic valuation of an integer $m$ . Motivated…

The complete cubic Walsh spectrum of a permutation-inverse Boolean family

A first-exit proof of Cusick's sum-of-digits conjecture

A proof of a permutation-inverse bent-function conjecture

Banded quadratic digit functions along irreducible polynomials over finite fields

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

On the 2-adic valuation of I¨k​(n)

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

On the $2$ -adic valuation of $I ¨ _{k} (n)$