Yue-Feng She

activity

20202026

most citedCyclotomic matrices and hypergeometric functions over finite fields

1 citations · 1 across the 16 of their papers we have counts for

collaborators

17 papers

math.CO2026

A Conjecture on Circular Permutations over Finite Fields

Xin-Qi Luo, Yue-Feng She

Let $\mathbb{F}_q$ be a finite field with $q>7$. Zhi-Wei Sun conjectured that for every $a_0\in\mathbb{F}_q$, there is a circular permutation $(a_1,\dots,a_{q-1})$ of non-z…

math.CO2026

Proof of a conjecture on permutations

Yue-Feng She, Xin-Qi Luo

Given a positive integer $n$ , define a function on the symmetric group $S_{n}$ by $F (τ) = k = 1 \sum n k^{2} τ (k)^{2} .$ Motivated by a conjecture of Zhi-Wei Sun, we investigate the res…

math.NT2026

Representations of positive integers by three almost-prime squares

Yue-Feng She, Yu-Chen Sun, Guang-Liang Zhou

Let $P_{r}$ denote an integer with at most $r$ prime factors, counted with multiplicity. It is known that every sufficiently large integer $N$ satisfying $N \equiv 3 (mod 24)$ and $…

math.NT2025

On restricted sums of four squares and Zhi-Wei Sun's $x + 24 y$ conjecture

Hai-Liang Wu, Yue-Feng She

In this paper, by using the arithmetic theory of ternary quadratic forms, we study some refinements on Lagrange's four-square theorem. For example, given positive integers $a, b$ sa…

math.NT2024

Some determinants involving binary forms

Yue-Feng She, Zhi-Wei Sun

In this paper, we study arithmetic properties of certain determinants involving powers of $i^{2} + c ij + d j^{2}$ , where $c$ and $d$ are integers. For example, for any odd integer $n > 1$ wit…

math.NT2022

Trinomial coefficients and related matrices over finite fields

Yue-Feng She, Hai-Liang Wu

In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields…

math.CO2022

A novel permanent identity with applications

Yue-Feng She, Zhi-Wei Sun, Wei Xia

Let $n$ be a positive integer, and define the rational function $S (x_{1}, \dots, x_{2 n})$ as the permanent of the matrix $[x_{j, k}]_{1 \leq j, k \leq 2 n}$ , where $$x_{j,k}=\begin{cases}(x_…

math.NT2022

Additive decompositions of cubes in finite fields

Hai-Liang Wu, Yue-Feng She

Let $p \equiv 1 (mod 3)$ be a prime . We study several topics on additive decompositions concerning the set $C_{p}$ of all non-zero cubes in the finite field of $p$ elements. For example…

math.NT2022

On additive decompositions of primitive elements in finite fields

Hai-Liang Wu, Yue-Feng She

In this paper, we study several topics on additive decompositions of primitive elemements in finite fields. Also we refine some bounds obtained by Dartyge and Sárközy and Shparlins…

math.NT2021★ 1 cited

Cyclotomic matrices and hypergeometric functions over finite fields

Hai-Liang Wu, Yue-Feng She, Li-Yuan Wang

With the help of hypergeometric functions over finite fields, we study some arithmetic properties of cyclotomic matrices involving characters and binary quadratic forms over finite…

math.NT2021

A conjecture of Zhi-Wei Sun on determinants over finite fields

Hai-Liang Wu, Yue-Feng She, He-Xia Ni

In this paper, we study certain determinants over finite fields. Let $F_{q}$ be the finite field of $q$ elements and let $a_{1}, a_{2}, \dots, a_{q - 1}$ be all nonzero elements of…

math.NT2021

Cubes in finite fields and related permutations

Hai-Liang Wu, Yue-Feng She

Let $p = 3 n + 1$ be a prime with $n \in N = {0, 1, \dots}$ , and let $g \in Z$ be a primitive root modulo $p$ . Let $0 < a_{1} < \dots < a_{n} < p$ be all the cubic residues modulo $p$ …

math.NT2021

Primitive elements and $k$ -th powers in finite fields

Hai-Liang Wu, Yue-Feng She

Let $F_{q}$ be the finite field of $q$ elements, and let $k ∣ q - 1$ be a positive integer. Let $f (x) = a x^{2} + b x + c$ be a quadratic polynomial in $F_{q} [x]$ with $b^2-4ac…

math.NT2020

Sums of four squares with a certain restriction

Yue-Feng She, Hai-Liang Wu

In 2016, while studying restricted sums of integral squares, Sun posed the following conjecture: Every positive integer $n$ can be written as $x^{2} + y^{2} + z^{2} + w^{2}$ $(x,y,z,w\in\mathbb{…

math.NT2020

Numbers represented by restricted sums of four squares

Guang-Liang Zhou, Yue-Feng She

In this paper, we prove some results of restricted sums of four squares using arithmetic of quaternions in the ring of Lipschitz integers. For example, we show that every nonnegati…

math.NT2020

Jacobsthal sums and permutations of biquadratic residues

Hai-Liang Wu, Yue-Feng She

Let $p \equiv 1 (mod 4)$ be a prime. In this paper, with the help of Jacobsthal sums, we study some permutation problems involving biquadratic residues modulo $p$ .

math.NT2020

On a polynomial involving roots of unity and its applications

Hai-Liang Wu, Yue-Feng She

Let $p > 3$ be a prime. Gauss first introduced the polynomial $S_{p} (x) = \prod_{c} (x - ζ_{p}^{c}),$ where $0 < c < p$ and $c$ varies over all quadratic residues modulo $p$ and $ζ_{p} = e^{2 π i / p}$ . La…

A Conjecture on Circular Permutations over Finite Fields

Proof of a conjecture on permutations

Representations of positive integers by three almost-prime squares

On restricted sums of four squares and Zhi-Wei Sun's x+24y conjecture

Some determinants involving binary forms

Trinomial coefficients and related matrices over finite fields

A novel permanent identity with applications

Additive decompositions of cubes in finite fields

On additive decompositions of primitive elements in finite fields

Cyclotomic matrices and hypergeometric functions over finite fields

A conjecture of Zhi-Wei Sun on determinants over finite fields

Cubes in finite fields and related permutations

Primitive elements and k-th powers in finite fields

Sums of four squares with a certain restriction

Numbers represented by restricted sums of four squares

Jacobsthal sums and permutations of biquadratic residues

On a polynomial involving roots of unity and its applications

On restricted sums of four squares and Zhi-Wei Sun's $x + 24 y$ conjecture

Primitive elements and $k$ -th powers in finite fields