Exploring the magic of numbers
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.
Associated schools, institutes & centres
Study with us
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 t.trudgian@adfa.edu.au, opens in a new window.
We particularly encourage female mathematicians to apply.
Our researchers
-
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, opens in a new window to publish work and organise joint conferences. We visit Sydney regularly and also travel to stimulating meetings in Australia, including Number Theory Down Under, opens in a new window and the December meeting of the Australian Mathematical Society, opens in a new window.
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!
-
Garcia, S. R., Lee, E. S., 2022, Unconditional explicit Mertens’ theorems for number fields and Dedekind zeta residue bounds, opens in a new window, The Ramanujan Journal 57: 1169–1191.
Chen, C., Kerr, B., Maynard, J. and Shparlinski, I. E., 2022, Metric theory of Weyl sums, opens in a new window. Mathematische Annalen (in press).
Johnston, D,, 2022, On the average value of π(t)-li(t), opens in a new window. 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, opens in a new window, 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)|, opens in a new window, Journal of Number Theory 240: 641–655.
Booker, A. R., Hathi, S., Mossinghoff, M. J. and Trudgian, T. S., 2022, Wolstenholme and Vandiver primes, opens in a new window. 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, opens in a new window, Journal of Number Theory 231: 464-491.
Francis, F. J., Lee, E. S., 2022, Additive representations of natural numbers, opens in a new window, Integers, 22, #A14, pp. 1–10.
Kerr, B., Mérai, L., and Shparlinski, I. E., 2021, On digits of Mersenne numbers, opens in a new window. Revista Matemática Iberoamericana (in press).
Bordignon, M., 2021, Partial Gaussian sums and the Pólya–Vinogradov inequality for primitive characters, opens in a new window, Revista Matemática Iberoamericana 38, no. 4, pp. 1101–1127
Cully-Hugill, M.; T Trudgian, 2021, Two explicit divisor sums, opens in a new window, The Ramanujan Journal 56.1: 141-149.
Lee, E. S., 2021, On an explicit zero-free region for the Dedekind zeta-function, opens in a new window, Journal of Number Theory 224: 307-322.
Francis, F. J., 2021, An investigation into explicit versions of Burgess' bound, opens in a new window, Journal of Number Theory, 228, 87-107.
Kobayashi M; Trudgian T, 2020, 'On integers n for which σ(2n + 1)≥σ(2n), opens in a new window', Journal of Number Theory, vol. 215, pp. 138 – 148
Kerr B; McGown KJ; Trudgian T, 2020, 'The least primitive root modulo p2, opens in a new window', Journal of Number Theory, vol. 215, pp. 20 – 27
McGown KJ; Trudgian T, 2020, 'Explicit upper bounds on the least primitive root, opens in a new window', Proceedings of the American Mathematical Society, vol. 148, pp. 1049 – 1061
Simonič A, 2020, 'On Littlewood's proof of the prime number theorem, opens in a new window', Bulletin of the Australian Mathematical Society, vol. 101, pp. 226 – 232
Bordignon M, 2020, 'Explicit bounds on exceptional zeroes of Dirichlet L-functions II, opens in a new window', 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, opens in a new window. J. Math. Anal. Appl. 491, no. 1, opens in a new window, 124303, 41 pp.
Akbary, Amir; Francis, Forrest J., 2020, Euler's function on products of primes in a fixed arithmetic progression, opens in a new window. Math. Comp. 89, no. 322, opens in a new window, 993–1026
Bordignon M, 2019, 'Explicit bounds on exceptional zeroes of Dirichlet L-functions, opens in a new window', Journal of Number Theory, vol. 201, pp. 68 – 76
Starichkova V, 2018, 'Global bifurcations in generic one-parameter families on S^2', opens in a new window, 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:
- Sarah Peluse, University of Michigan, December 2023
- Roger Heath-Brown, Oxford, December 2023
- Vandita Patel, University of Manchester, September 2023
- Nikita Shulga, La Trobe University, September 2023
- Gerardo Gonzalez Robert, La Trobe University, September 2023
- Laura Paladino, University of Calabria, August 2023
- Lee Zhao, UNSW Sydney, May 2023
- Neea Palojärvi, University of Helsinki, March 2023
- June Park, University of Melbourne, November 2022
- Noa Kraitzman, Macquarie University, October 2022
- Randell Heyman, opens in a new window, UNSW Sydney, October 2022
- Angus McAndrew, ANU, September 2022
- Ayreena Bakhtawar, Scuola Normale Superiore, August 2022
- Anna Romanov, UNSW Sydney, August 2022
- Adam Logan, Tutte Institute and Carleton University, February 2020
- Raph Steiner, opens in a new window, Institute for Advanced Study, February 2020
- Thomas Bloom, University of Cambridge, January 2020
- Ayla Gafni, University of Mississippi, January 2020
- Holly Krieger, University of Cambridge, November 2019
- Kam Hung Yau, UNSW Sydney, November 2019
- Enrique Treviño, opens in a new window, Lake Forest College, October 2019
- Peter Humphries, University College, London, September 2019
- Olivier Ramaré, Aix Marseille University, September 2019
- Changhao Chen, UNSW Sydney, April 2019
- Asif Zaman, Stanford University, March 2019
- Kevin McGown, California State University, Chico, January-March 2019
- Micah Milinovich, University of Mississippi, January 2019
- Greg Martin, University of British Columbia, November 2018
- Dave Platt, University of Bristol, September 2018
- Chacha Suriajaya, RIKEN, September 2018
- Caroline Turnage-Butterbaugh, Carleton College, March 2018
- Adrian Dudek, University of Queensland, May 2024
Please get in touch if you would like to visit and we can arrange a seminar.
- Sarah Peluse, University of Michigan, December 2023