Number theory

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!

• Timothy Trudgian
• Bryce Kerr
• Aleksander Simonic
• Valeriia Starichkova
• Daniel Johnston
• Nicol Leong
• Andrew Yang
• Dion Nikolic
• Chiara Bellotti
• Riddhi Manna
• Sebastian Tudzi
• Dion Nikolic
• Chiara Bellotti
• Shashi Chourasiya
• Jordan Pertile
• En Ci Nicol Leong
• Gustav Bagger
• Liang Wang
• Ali Ebadi

• 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

• Thomas Morrill, Trine University
• Matteo Bordignon, KTH Stockholm
• Ethan Lee, University of Bristol
• Forrest Francis, Deakin University
• Shehzad Hathi, Macquarie Group
• Michaela Cully-Hugil, Maquarie Group

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, 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, 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, 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.