Seth Hardy

collaborators

3 papers

math.NT2026

Character sums over smooth numbers

Seth Hardy, Max Wenqiang Xu

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

math.NT2026

Helson's conjecture for smooth numbers

Seth Hardy, Max Wenqiang Xu

Let $I^¨ (x, y)$ denote the count of $y$ -smooth numbers below $x$ and $P (n)$ denote the largest prime factor of $n$ . We prove that for $f$ a Steinhaus random multiplicative function,…

math.NT2025

The distribution of partial sums of random multiplicative functions with a large prime factor

Seth Hardy

For $f$ a Steinhaus random multiplicative function, we prove convergence in distribution of the appropriately normalised partial sums \[ \frac{{(\log \log x)}^{1/4}}{\sqrt{x}} \sum…