Author

M. Xu

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Open access Sep 2026

The largest support to escape chaos in random multiplicative functions.

Let [Formula: see text] be a Steinhaus random multiplicative function and let [Formula: see text] be a finite set of integers. We show that convergence of [Formula: see text] to a standard complex normal distribution forces [Formula: see text]. We prove that this zero-density condition is sharp: For most sets [Formula:...

M. Xu · Proceedings of the National... · 0 citations

Preprint Sep 2026

Maximising the number of solutions to linear equations

We study the asymptotically maximal possible number of integer solutions to the linear equation $ax+by+cz = 0$ with a fixed choice of $a, b, c \in \mathbb{Z}$ and variables $x, y, z \in S$ for some finite set $S\subset \mathbb{Z}$, as $|S|\to +\infty$. Define $\gamma_{a, b, c}$ to be the largest constant for which ther...

Žarko Ranđ Elović, Xuan-Cheng Shao, M. Xu et al. · 0 citations