Zhi-Wei Sun

collaborators

9 papers

math.NT2026

On Diophantine equations over the integer rings of quadratic fields

Zhi-Wei Sun

Let $K$ be any quadratic number field, and let $O_{K}$ be the ring of algebraic integers in $K$ . In 1975 J. Denef proved that Hilbert's Tenth Problem over $O_{K}$ has a negative soluti…

math.NT2026

$Q ∖ Z$ is diophantine over $Q$ with $7$ unknowns

Zhi-Wei Sun

The paper proves that the set of non‑integer rational numbers is diophantine over ℚ using a polynomial with only seven auxiliary variables, improving the previous bound of ten and…

math.NT2026

A new kind of numbers and related congruences

Zhi-Wei Sun

The paper introduces a family of numbers defined by sums of powers of multinomial coefficients, proves a general prime-modulus congruence for them, and verifies a conjectured congr…

math.NT2026

On zero-sum problems of new types

Zhi-Wei Sun

In this paper, we investigate zero-sum problems of new types. For example, given $2 n - 1$ integers $a_{1}, \dots, a_{2 n - 1}$ not divisible by an integer $n > 1$ , we prove that for some non…

math.CO2026

Exterior Algebra and an Extension of the Feng-Sun-Xiang Theorem in $p$ -groups

Zhi-Wei Sun, Lilu Zhao

Let $G$ be a finite group with $∣ G ∣ = p^{m}$ where $p$ is a prime and $m$ is a positive integer. Let $k < p$ . Let $a_{1}, \dots, a_{k} \in G$ be pairwise distinct and let $b_{1}, \dots, b_{k} \in G$ …

math.NT2026

Supercongruences for central trinomial coefficients

Hao Pan, Zhi-Wei Sun

For each $n = 0, 1, 2, \dots$ , the central trinomial coefficient $T_{n}$ is the coefficient of $x^{n}$ in the expansion of $(x^{2} + x + 1)^{n}$ . Let $p > 3$ be a prime, and let $n$ be any positive…

On Diophantine equations over the integer rings of quadratic fields

Q∖Z is diophantine over Q with 7 unknowns

A new kind of numbers and related congruences

On zero-sum problems of new types

Exterior Algebra and an Extension of the Feng-Sun-Xiang Theorem in p-groups

Supercongruences for central trinomial coefficients

$Q ∖ Z$ is diophantine over $Q$ with $7$ unknowns

Exterior Algebra and an Extension of the Feng-Sun-Xiang Theorem in $p$ -groups