Seth Hardy

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20232026

most citedAlmost sure bounds for a weighted Steinhaus random multiplicative function

2 citations · 3 across the 5 of their papers we have counts for

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math.NT2025

Helson's conjecture for smooth numbers

Seth Hardy, Max Wenqiang Xu

Let $Ψ (x, y)$ 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, t…

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…