A. Walker

activity

20152024

most citedThe primes are not metric Poissonian

22 citations · 53 across the 11 of their papers we have counts for

collaborators

15 papers

math.NT2024

Proving the Duffin-Schaeffer conjecture without GCD graphs

Manuel Hauke, Santiago Vazquez Saez, Aled Walker

We present a novel proof of the Duffin-Schaeffer conjecture in metric Diophantine approximation. Our proof is heavily motivated by the ideas of Koukoulopoulos-Maynard's breakthroug…

math.NT2023★ 1 cited

On a Bohr set analogue of Chowla's conjecture

Joni Teräväinen, Aled Walker

Let $λ$ denote the Liouville function. We show that the logarithmic mean of $λ (⌊ α_{1} n ⌋) λ (⌊ α_{2} n ⌋)$ is $0$ whenever $α_{1}, α_{2}$ are positive reals with $α_1/α_…

math.CO2021

Effective results on the size and structure of sumsets

Andrew Granville, George Shakan, Aled Walker

Let $A \subset Z^{d}$ be a finite set. It is known that $N A$ has a particular size ( $∣ N A ∣ = P_{A} (N)$ for some $P_{A} (X) \in Q [X]$ ) and structure (all of the l…

math.NT2021

Correlations of sieve weights and distributions of zeros

Aled Walker

In this note we give two small results concerning the correlations of the Selberg sieve weights. We then use these estimates to derive a new (conditional) lower bound on the varian…

math.NT2020★ 3 cited

Extremal problems for GCDs

Ben Green, Aled Walker

We prove that if $A \subseteq [X, 2 X]$ and $B \subseteq [Y, 2 Y]$ are sets of integers such that $g cd (a, b) \geq D$ for at least $δ ∣ A ∣∣ B ∣$ pairs $(a, b) \in A \times B$ then $|A||B|…

math.NT2020

A tight structure theorem for sumsets

Andrew Granville, Aled Walker

Let $A = {0 = a_{0} < a_{1} < \dots < a_{ℓ + 1} = b}$ be a finite set of non-negative integers. We prove that the sumset $N A$ has a certain easily-described structure, provided t…