M. Xu

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math.NT2026

Distribution of random multiplicative functions in short intervals, with proper normalization

Adam J. Harper, Kannan Soundararajan, Max Wenqiang Xu

We determine the limiting distribution of partial sums of a Steinhaus random multiplicative function $\sum_{x \leq n \leq x + y} f (n)$ over short intervals $[x, x + y]$ , where $y \rightar…

math.NT2024

A polynomial with a root mod $p$ for every $p$ has a real root

Rodrigo Angelo, Max Wenqiang Xu

We prove that if a polynomial has a root mod $p$ for every large prime $p$ , then it has a real root. As an application, we show that the primes can't be covered by finitely many po…

Distribution of random multiplicative functions in short intervals, with proper normalization

A polynomial with a root mod p for every p has a real root

A polynomial with a root mod $p$ for every $p$ has a real root