Preprints
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)