Christopher Atherfold

collaborators

3 papers

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.PR2025

The Fourier coefficients of the critical holomorphic multiplicative chaos

Christopher Atherfold, Joseph Najnudel

The holomorphic multiplicative chaos (HMC) is a holomorphic analogue of the Gaussian multiplicative chaos. It arises naturally as the limit in large matrix size of the characterist…

math.NT2025

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 $ε > 0$ , then $\sum_{n ⩽ x} \frac{f ( n )}{n} ≪ (lo g lo g (x))^{3/4 + ε}$ for almost all $f$ .…

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

The Fourier coefficients of the critical holomorphic multiplicative chaos

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