Christopher Atherfold

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math.NT2026

On the $β = 2$ Partition function for Dirichlet $L$ -functions in the $q$ -aspect

Christopher Atherfold

We study the $β = 2$ partition function $\int_{∣ h ∣ \leq l o g^{θ} (q) /2} ∣ L (1/2 + ih, χ) ∣^{2} d h$ for typical Dirichlet characters modulo a large prime $q$ and $θ \in (- 1/2, 0]$ motivated by a $q…

math.NT2026

Almost sure bounds for weighted sums of Rademacher random multiplicative functions

Christopher Atherfold

We prove that when $f$ is a Rademacher random multiplicative function for any $I^µ > 0$ , then $\sum_{n ⩽ x} \frac{f ( n )}{n} ≪ (lo g lo g (x))^{3/4 + I^µ}$ for almost all $f$ …

On the β=2 Partition function for Dirichlet L-functions in the q-aspect

Almost sure bounds for weighted sums of Rademacher random multiplicative functions

On the $β = 2$ Partition function for Dirichlet $L$ -functions in the $q$ -aspect