Adam J Harper

collaborators

2 papers

math.NT2026

Lower bounds for low moments of character sums, I: Short sums with general multiplicative weights

Adam J. Harper

We establish sharp lower bounds for the Dirichlet character moments $\frac{1}{r - 1} \sum_{I ¨ mod r} ∣ \sum_{n \leq x} I ¨ (n) ∣^{2 q}$ , where $r$ is a large prime, $1 \leq x…

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…