Number Theory is one of the oldest branches of pure mathematics and is concerned with the structure of natural numbers (e.g. 1, 2, 3, 4). Number theorists study prime numbers (2, 3, 5, 7, etc.) as well as the properties of positive integers. Elementary number theory tackles questions using properties of numbers directly and is used to solve equations with rational or integer solutions. Analytic number theory relies on tools from calculus and analysis.
Modern number theory research at UNSW Canberra uses a mix of these two methods, often flavoured with a computational component of research.
Garcia, S. R., Lee, E. S., 2022, Unconditional explicit Mertens’ theorems for number fields and Dedekind zeta residue bounds, The Ramanujan Journal 57: 1169–1191.
Chen, C., Kerr, B., Maynard, J. and Shparlinski, I. E., 2022, Metric theory of Weyl sums. Mathematische Annalen (in press).
Johnston, D,, 2022, On the average value of π(t)-li(t). Canadian Mathematical Bulletin (in press)
Simonič, A., Trudgian, T. and Turnage-Butterbaugh, C., 2022, Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function, Transactions of the American Mathematical Society, 375(05), pp.3239-3265.
Mossinghoff, M. J., Starichkova, V. V. and Trudgian, T. S., 2022 Explicit lower bounds on| L (1, χ)|, Journal of Number Theory 240: 641–655.
Booker, A. R., Hathi, S., Mossinghoff, M. J. and Trudgian, T. S., 2022, Wolstenholme and Vandiver primes. The Ramanujan Journal, 58(3), 913-941.
Simonič, A., 2022, On explicit estimates for S (t), S1 (t), and ζ (1/2+ it) under the Riemann hypothesis, Journal of Number Theory 231: 464-491.
Francis, F. J., Lee, E. S., 2022, Additive representations of natural numbers, Integers, 22, #A14, pp. 1–10.
Kerr, B., Mérai, L., and Shparlinski, I. E., 2021, On digits of Mersenne numbers. Revista Matemática Iberoamericana (in press).
Bordignon, M., 2021, Partial Gaussian sums and the Pólya–Vinogradov inequality for primitive characters, Revista Matemática Iberoamericana 38, no. 4, pp. 1101–1127
Cully-Hugill, M.; T Trudgian, 2021, Two explicit divisor sums, The Ramanujan Journal 56.1: 141-149.
Lee, E. S., 2021, On an explicit zero-free region for the Dedekind zeta-function, Journal of Number Theory 224: 307-322.
Francis, F. J., 2021, An investigation into explicit versions of Burgess' bound, Journal of Number Theory, 228, 87-107.
Kobayashi M; Trudgian T, 2020, 'On integers n for which σ(2n + 1)≥σ(2n)', Journal of Number Theory, vol. 215, pp. 138 – 148
Kerr B; McGown KJ; Trudgian T, 2020, 'The least primitive root modulo p2', Journal of Number Theory, vol. 215, pp. 20 – 27
McGown KJ; Trudgian T, 2020, 'Explicit upper bounds on the least primitive root', Proceedings of the American Mathematical Society, vol. 148, pp. 1049 – 1061
Simonič A, 2020, 'On Littlewood's proof of the prime number theorem', Bulletin of the Australian Mathematical Society, vol. 101, pp. 226 – 232
Bordignon M, 2020, 'Explicit bounds on exceptional zeroes of Dirichlet L-functions II', Journal of Number Theory, vol. 210, pp. 481 – 487
Simonič, Aleksander, 2020, Explicit zero density estimate for the Riemann zeta-function near the critical line. J. Math. Anal. Appl. 491, no. 1, 124303, 41 pp.
Akbary, Amir; Francis, Forrest J., 2020, Euler's function on products of primes in a fixed arithmetic progression. Math. Comp. 89, no. 322, 993–1026
Bordignon M, 2019, 'Explicit bounds on exceptional zeroes of Dirichlet L-functions', Journal of Number Theory, vol. 201, pp. 68 – 76
Starichkova V, 2018, 'Global bifurcations in generic one-parameter families on S^2', Regular and chaotic dynamics, vol. 23, no. 6, pp. 767-784
We proudly host a range of high-calibre visitors to the university. Recent visits include:
Please get in touch if you would like to visit and we can arrange a seminar.
We have a vibrant group of students and faculty in number theory. Our students, from seven different countries, collaborate with each other and with the visitors we regularly host at our department. Students also pursue their own research, focussing on a mixture of reading classical and modern texts and tackling unsolved problems early in their PhDs.
We work closely with our colleagues in the number theory group UNSW Sydney to publish work and organise joint conferences. We visit Sydney regularly and also travel to stimulating meetings in Australia, including Number Theory Down Under and the December meeting of the Australian Mathematical Society.
Since UNSW Canberra provides generous travel support to researchers, several of our students and faculty may have the opportunity to attend overseas conferences. Students can also take advantage of Canberra’s location, and in their holidays travel to many beautiful scenic locations in Australia: an absolute must!
We offer PhD programs in mathematics and statistics and actively encourage new applications. Scholarships of $35,000 (AUD) are available for PhD applicants who achieved H1 (High Distinction) in their undergraduate program and have completed a Master by Research. If you are interested in applying, please contact email@example.com.
We particularly encourage female mathematicians to apply.