Huixi Li

activity

20192026

collaborators

11 papers

math.NT2026

$6$ powers of $2$ in the Linnik--Goldbach problem

Huixi Li, Zhixin Liu

Linnik's approximation to Goldbach's conjecture concerns the representation of sufficiently large even integers as the sum of two primes and a bounded number of powers of two. We p…

math.NT2026

A Romanoff-type theorem for $P_{2}$ +{ $a^{a}$ : a $\geq$ 1}

Yuchen Ding, Huixi Li, Junfeng Li

Let $Ω (n)$ denote the number of prime factors of $n$ , counted with multiplicity, and put $P_{2}$ ={ $m$ $\geq$ 1: $Ω (m)$ $\leq$ 2}. We prove that the sumset $P_{2}$ +{ $a^{a}$ : a $\geq$ 1} has po…

math.NT2026

Adjacent comparison bounds and extremal sets for Ruzsa numbers

Yuchen Ding, Huixi Li, Junfeng Li +2

Let $m$ be a positive integer and $Z_{m}$ the residue class ring modulo $m$ . The Ruzsa number $R_{m}$ is defined to be the least integer $r$ such that there is a subset $\math…

math.NT2026

An Improvement of Konstantoulas' Density Constant

Huixi Li, Zihan Zhang

Let $A \subset N$ , and define its ordered representation function $r (n) = # {(a, b) \in A \times A : a + b = n} .$ The Erdos--Turan conjecture asserts that, if $r (n) > 0$ for all sufficiently…

math.NT2025

Note on a conjecture of Sárközy on special sequences

Yuchen Ding, Huixi Li, Zihan Zhang

Let $α > 1$ be an irrational number and $k \geq 2$ a positive integer. Let $f (x)$ be a polynomial with positive integer coefficients. Solving a 2001 problem of Sárközy on special seque…

math.NT2023

On covering systems of polynomial rings over finite fields

Huixi Li, Biao Wang, Chunlin Wang +1

In 1950, Erdős posed a question known as the minimum modulus problem on covering systems for $Z$ , which asked whether the minimum modulus of a covering system with distinc…

math.NT2023

Some discussions on the Goldbach conjecture

Huixi Li

According to some discussions based on syllogism, we present results on the binary Goldbach conjecture in three categories: results that are weaker than the Goldbach conjecture, su…

math.NT2023

On the minimum modulus problem in number fields

Huixi Li, Biao Wang, Shaoyun Yi

The minimum modulus problem on covering systems was posed in 1950 by Erdős, who asked whether the minimum modulus of a covering system with distinct moduli is bounded. In 2007, Fil…

math.NT2020

On the connection between the Goldbach conjecture and the Elliott-Halberstam conjecture

Jing-Jing Huang, Huixi Li

In this paper we prove that the binary Goldbach conjecture for sufficiently large even integers would follow under the assumption that both the Elliott-Halberstam conjecture and a…

math.NT2019

On a generalization of a theorem of Popov

Jing-Jing Huang, Huixi Li

In this paper, we obtain sharp estimates for the number of lattice points under and near the dilation of a general parabola, the former generalizing an old result of Popov. We appl…

math.NT2019

On two lattice points problems about the parabola

Jing-Jing Huang, Huixi Li

We obtain asymptotic formulae with optimal error terms for the number of lattice points under and near a dilation of the standard parabola, the former improving upon an old result…

6 powers of 2 in the Linnik--Goldbach problem

A Romanoff-type theorem for P2​+{aa: a≥ 1}

Adjacent comparison bounds and extremal sets for Ruzsa numbers

An Improvement of Konstantoulas' Density Constant

Note on a conjecture of Sárközy on special sequences

On covering systems of polynomial rings over finite fields

Some discussions on the Goldbach conjecture

On the minimum modulus problem in number fields

On the connection between the Goldbach conjecture and the Elliott-Halberstam conjecture

On a generalization of a theorem of Popov

On two lattice points problems about the parabola

$6$ powers of $2$ in the Linnik--Goldbach problem

A Romanoff-type theorem for $P_{2}$ +{ $a^{a}$ : a $\geq$ 1}