Lilu Zhao

activity

20082026

most citedSums of four squares of primes

6 citations · 19 across the 20 of their papers we have counts for

collaborators

24 papers

math.NT2026

Translation invariant quadratic forms in $8$ variables and dense sets of primes

Zhaochen Pei, Maoru Tan, Weiwen Zhang +1

Let $Q$ be a translation invariant indefinite quadratic form in $8$ variables. Let $P$ be the set of all primes. Let $A \subset P \cap {1, \dots, X}$ . By…

math.CO2026

On additive complements in natural numbers

Quan-Hui Yang, Lilu Zhao

We prove that for additive complements $A$ and $B$ , if $x \to + \infty lim sup \frac{A ( x ) B ( x )}{x} < \frac{4}{3},$ then $A (x) B (x) - x \to + \infty (x \to + \infty) .$ This impro…

math.CO2026

Products of Two Integers Avoiding Perfect Powers

Quan-Hui Yang, Lilu Zhao

For integers $d \geq 3$ , let $F_{2, d} (n)$ be the largest size of a subset of $[n]$ containing no two distinct elements whose product is a perfect $d$ -th power, and let $f_{2, d} (n)$ …

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.NT2023

A new upper bound on Ruzsa's number on the Erd\H os-Turán conjecture

Yuchen Ding, Lilu Zhao

In this note, we show that the Ruzsa number $R_{m}$ is bounded by $192$ for any positive integer $m$ , which improved the prior bound $R_{m} \leq 288$ given by Y.--G. Chen in 2008.

math.NT2023

Solution to a problem of Luca, Menares and Pizarro-Madariaga

Yuchen Ding, Lilu Zhao

Let $k \geq 2$ be a positive integer and $P^{+} (n)$ the greatest prime factor of a positive integer $n$ with convention $P^{+} (1) = 1$ . For any $θ\in \left[\frac 1{2k},\frac{17}{32k}\right…

Translation invariant quadratic forms in 8 variables and dense sets of primes

On additive complements in natural numbers

Products of Two Integers Avoiding Perfect Powers

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

A new upper bound on Ruzsa's number on the Erd\H os-Turán conjecture

Solution to a problem of Luca, Menares and Pizarro-Madariaga

Translation invariant quadratic forms in $8$ variables and dense sets of primes

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