Number Theory

Timothy Trudgian
Bryce Kerr
Aleksander Simonic
Shehzad Hathi
Michaela Cully-Hugill
Valeriia Starichkova
Daniel Johnston
Nicol Leong
Andrew Yang
Dion Nikolic
Chiara Bellotti

Thomas Morrill, Trine University 

Matteo Bordignon, Charles University

Ethan Lee, University of Bristol

Forrest Francis, Deakin University

• 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: 

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

Raph Steiner, Institute for Advanced Study, February 2020 

Adam Logan, Tutte Institute and Carleton University, 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   

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!