## Research

Broadly, my area of research is analytic number theory. I am interested in biases, oscillations and sign changes in arithmetic functions while on the additive side, I am interested in the application of the circle method to problems of representation of natural numbers as sums of primes (or prime powers). The source code for some of the computations in the work below can be found here.

## Publications and Preprints

- Wolstenholme and Vandiver primes (with M. Mossinghoff and T. Trudgian):
*The Ramanujan Journal 58, 913–941 (2022)*. Journal version. - Representation of even integers as a sum of squares of primes and powers of two:
*Acta Arithmetica 206 (2022)*. Journal version. - On the sum of a prime and a square-free number with divisibility conditions (with D. R. Johnston): Preprint on arXiv.
- Mertens' third theorem for number fields: A new proof, Cramér's inequality, oscillations, and bias (with E. S. Lee): Preprint on arXiv.

## Selected Talks

- AustMS 2019 [NT & AG Special Session] (Dec '19) - Biases, oscillations & first sign changes: Presentation
- NTDU 8 (Oct '20) - Wolstenholme and Vandiver primes: Presentation
- NTDU 9 (Sep '21) - Representation of even integers as a sum of squares of primes and powers of two: Presentation