Adam J Harper

activity

20102026

most citedSharp conditional bounds for moments of the Riemann zeta function

57 citations · 242 across the 23 of their papers we have counts for

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2 papers · 1 filter

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 $\frac{1}{r - 1} \sum_{χ mod r} ∣ \sum_{n \leq x} χ (n) ∣^{2 q}$ , where $r$ is a large prime, $1 \leq x \l…

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…