Max Xu

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20212026

most citedPaucity phenomena for polynomial products

3 citations · 4 across the 8 of their papers we have counts for

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4 papers · 1 filter

math.NT2026

The typical size of Hecke eigenvalue sums is $o (x)$

Max Wenqiang Xu, Junren Zheng

Let $H_{k}$ denote the set of normalized holomorphic Hecke cusp forms of weight $k$ for the full modular group $SL_{2} (Z)$ . For each $f \in H_{k}$ , le…

math.NT2026

Random Multiplicative Functions and Making Squares from Polynomial Values

Régis de la Bretèche, Victor Y. Wang, Max Wenqiang Xu

For a large family of polynomials $P (X) \in Z [X]$ , we prove central limit theorems for $\sum_{n \leq N} f (P (n))$ for both Rademacher and extended Rademacher multiplicative fu…

math.NT2026

Character sums over smooth numbers

Seth Hardy, Max Wenqiang Xu

Let $Ψ (x, y)$ denote the count of $y$ -smooth numbers below $x$ and $P (n)$ denote the largest prime factor of $n$ . We show that \[ \frac{1}{φ(q)} \sum_{χ\bmod q} \Bigl| \sum_{\substa…

math.NT2026

Escaping Chaos in Random Multiplicative Functions

Max Wenqiang Xu

Let $f (n)$ be a Steinhaus random multiplicative function. Let $A \subset [1, N]$ be a finite set of integers. We show that \[\frac{1}{\sqrt{|A|}} \sum_{n\in A} f(n) \xrightarrow[]{d…

The typical size of Hecke eigenvalue sums is o(x​)

Random Multiplicative Functions and Making Squares from Polynomial Values

Character sums over smooth numbers

Escaping Chaos in Random Multiplicative Functions

The typical size of Hecke eigenvalue sums is $o (x)$