Preprints
The reverse Goldbach problem and a refined Zsiflaw–Legeis theorem (with M. Harm). (arXiv)
An update on the Linnik–Goldbach and Romanov problems (with T. Trudgian). (arXiv)
Primes and almost primes between cubes, submitted (with J. Sorenson, S. Thomas and J. Webster). (arXiv)
The infinitude of square-free palindromes, submitted (with B. Kerr). (arXiv)
An effective Bombieri–Vinogradov error term for sifting problems, submitted. (arXiv)
Zero-density estimates and the optimality of the error term in the prime number theorem, submitted. (arXiv)
Publications
A round of Pintz to celebrate oscillations in sums (with T. Trudgian),
Anal. Math., To appear. (arXiv)
New bounds and progress towards a conjecture on the summatory function of (-2)^Ω(n) (with N. Leong and S. Tudzi),
Exp. Math., To appear. (arXiv | journal)
New Explicit and Asymptotic Results in Sieve Theory,
Bull. Aust. Math. Soc., 2026 (full thesis | journal)
Evaluating and improving wave and non-wave stress parametrisations for oceanic flows (with C. Shakespeare and N. Constantinou),
J. Phys. Oceanogr., 2026. (arXiv | journal)
The sum of a prime power and an almost prime (with S. Thomas),
Forum Math., 2026. (arXiv | journal)
Almost primes between all squares (with A. Dudek),
J. Number Theory, 2026. (arXiv | journal)
Power-free palindromes and reversed primes (with S. Chourasiya),
Monatsh. Math., 2025. (arXiv | journal)
On the error term in the explicit formula of Riemann–von Mangoldt II (with M. Cully-Hugill),
Funct. Approx. Comment. Math., 2025. (arXiv | journal)
Some explicit results on the sum of a prime and an almost prime (with V. Starichkova),
Acta Math. Hungar., 2025. (arXiv | journal)
An explicit version of Chen's theorem and the linear sieve (with M. Bordignon and V. Starichkova),
Int. J. Number Theory, 2025. (arXiv | journal)
On the sum of a prime and a square-free number with divisibility conditions (with S. Hathi),
J. Number Theory, 2024. (arXiv | journal)
An explicit upper bound for L(1,χ) when χ is quadratic (with O. Ramaré and T. Trudgian),
Res. Number Theory, 2023. (arXiv | journal)
Some explicit estimates for the error term in the prime number theorem (with A. Yang),
J. Math. Anal. Appl., 2023. (arXiv | journal)
Exact formulae and Turán inequalities for Vafa–Witten invariants of K3 surfaces (with J. Males),
Proc. Edinb. Math. Soc., 2023. (arXiv | journal)
On the error term in the explicit formula of Riemann–von Mangoldt (with M. Cully-Hugill),
Int. J. Number Theory, 2023 . (arXiv | journal)
On the average value of π(t)-li(t),
Canad. Math. Bull., 2023. (arXiv | journal)
Improving bounds on prime counting functions by partial verification of the Riemann hypothesis,
Ramanujan J., 2022. (arXiv | journal)