Max Wenqiang Xu

collaborators

5 papers

math.CO2026

Almost Affine Invariance Over Prime Fields: Green Problem 90

Jie Ma, Quanyu Tang, Max Wenqiang Xu

Let $A \subset F_{p}$ with density 1/2. We call a set $A$ almost affine invariant under an affine transformation $I ¨ (x) = a x + b$ if \[|A \triangle Ï(A)| =o(p).\] We determine t…

math.NT2026

Oscillations of random multiplicative functions under initial bias

Rodrigo Angelo, Max Wenqiang Xu

We prove that if $f$ is a random completely multiplicative function, conditional $f (p) = 1$ for each prime $p \leq (lo g x)^{2 - I^µ}$ , the probability that $\sum_{1\le n \le N}f(n)\ge 0…

math.CO2026

Roth-type theorems in $K_{s, t}$ -free sets

Yifan Jing, Cosmin Pohoata, Max Wenqiang Xu

We show that for all integers $2 \leq s \leq t$ , any $K_{s, t}$ -free subset of $[N]$ with size $I^c ◯ (n^{1 - 1/ s})$ must contain a nontrivial solution to every fixed translation-invariant li…

math.NT2025

The distribution of prime values of random polynomials

Noah Kravitz, Katharine Woo, Max Wenqiang Xu

The Bateman--Horn Conjecture predicts how often an irreducible polynomial $f (x) \in Z [x]$ assumes prime values. We demonstrate that with sufficient averaging in the coeffi…