Dr Timothy Trudgian

+61 2 626 88021


Room 104 PEMS South (Bldg 26) School of Physical, Environmental and Mathematical Sciences, UNSW Canberra, Australian Defence Force Academy, PO Box 7916, Canberra BC ACT 2610, AUSTRALIA


BSc (Hons), The Australian National University, December 2005

DPhil, University of Oxford, June 2010

Research Interests: analytic number theory: the Riemann zeta-function, distribution of primes, primitive roots.

My CV; see also my UNSW Canberra website

I am part of the Number Theory Group at UNSW Canberra; I work closely with colleagues in number theory at UNSW Sydney.

Scholarships of $35,000 (AUD) are available for PhD applicants who achieved H1 (High Distinction) in their undergraduate programme and/or have completed a Masters by Research. If you are interested, please contact me at t.trudgian@adfa.edu.au. I particularly encourage female mathematicians to apply.

You can find out information about the PhD programme in mathematics here.

Note to international applicants: please read this website on English language requirements before contacting me.

Book Chapters

Mossinghoff M; Trudgian T, 2017, 'The Liouville function and the Riemann hypothesis', in Montgomery H; Nikeghbali A; Rassias M (ed.), Exploring the Riemann Zeta Function 190 years from Riemann's Birth, Springer, Cham, pp. 201 - 221

Journal articles

Kobayashi M; Trudgian T, 2020, 'On integers n for which σ(2n + 1)≥σ(2n)', Journal of Number Theory, http://dx.doi.org/10.1016/j.jnt.2020.02.007

Kerr B; McGown KJ; Trudgian T, 2020, 'The least primitive root modulo p2', Journal of Number Theory, http://dx.doi.org/10.1016/j.jnt.2020.01.002

McGown KJ; Trudgian T, 2020, 'Explicit upper bounds on the least primitive root', Proceedings of the American Mathematical Society, vol. 148, pp. 1049 - 1061, http://dx.doi.org/10.1090/proc/14800

Morrill T; Trudgian T, 2019, 'An elementary bound on Siegel zeroes', Journal of Number Theory, http://dx.doi.org/10.1016/j.jnt.2019.10.024

Bailey G; Cohen SD; Sutherland N; Trudgian T, 2019, 'Existence results for primitive elements in cubic and quartic extensions of a finite field', Mathematics of Computation, vol. 88, pp. 931 - 947, http://dx.doi.org/10.1090/mcom/3357

Cohen SD; Trudgian T, 2019, 'Lehmer numbers and primitive roots modulo a prime', Journal of Number Theory, vol. 203, pp. 68 - 79, http://dx.doi.org/10.1016/j.jnt.2019.03.004

Platt D; Trudgian T, 2019, 'Fujii's development on Chebyshev's conjecture', International Journal of Number Theory, vol. 15, pp. 639 - 644, http://dx.doi.org/10.1142/S1793042119500337

Munsch M; Trudgian T, 2018, 'Square-full primitive roots', International Journal of Number Theory, vol. 14, pp. 1013 - 1021, http://dx.doi.org/10.1142/S1793042118500604

Jarso T; Trudgian T, 2018, 'Quadratic non-residues that are not primitive roots', Mathematics of Computation, vol. 88, pp. 1251 - 1260, http://dx.doi.org/10.1090/MCOM/3378

Booker AR; Cohen SD; Sutherland N; Trudgian T, 2018, 'Primitive values of quadratic polynomials in a finite field', Mathematics of Computation, vol. 88, pp. 1903 - 1912, http://dx.doi.org/10.1090/mcom/3390

Cohen SD; Oliveira e Silva T; Sutherland N; Trudgian T, 2018, 'Linear combinations of primitive elements of a finite field', Finite Fields and their Applications, vol. 51, pp. 388 - 406, http://dx.doi.org/10.1016/j.ffa.2018.02.009

Cohen SD; Trudgian T, 2017, 'On the least square-free primitive root modulo p', Journal of Number Theory, vol. 170, pp. 10 - 16, http://dx.doi.org/10.1016/j.jnt.2016.06.011

Trudgian T; Wang Q, 2017, 'The T4 and G4 constructions of Costas arrays', Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 100, pp. 217 - 221

Platt DJ; Trudgian TS, 2017, 'On the sum of two squares and at most two powers of 2', American Mathematical Monthly, vol. 124, pp. 737 - 740, http://dx.doi.org/10.4169/amer.math.monthly.124.8.737

Cohen SD; Oliveira E Silva T; Trudgian T, 2016, 'On Grosswald's conjecture on primitive roots', Acta Arithmetica, vol. 172, pp. 263 - 270, http://dx.doi.org/10.4064/aa8109-12-2015

Trudgian T, 2016, 'Updating the error term in the prime number theorem', Ramanujan Journal, vol. 39, pp. 225 - 234, http://dx.doi.org/10.1007/s11139-014-9656-6

Cipu M; Trudgian T, 2016, 'Searching for Diophantine quintuples', Acta Arithmetica, vol. 173, pp. 365 - 382, http://dx.doi.org/10.4064/aa8254-2-2016

Trudgian TS, 2016, 'Improvements to Turing's Method II', Rocky Mountain Journal of Mathematics, vol. 46, pp. 325 - 332, http://dx.doi.org/10.1216/RMJ-2016-46-1-325

McGown K; Trevino E; Trudgian TS, 2016, 'Resolving Grosswald's conjecture on GRH', Functiones et Approximatio Commentarii Mathematici, vol. 55, pp. 215 - 225, http://dx.doi.org/10.7169/facm/2016.55.2.5

Platt DJ; Trudgian TS, 2016, 'Zeroes of partial sums of the zeta-function', LMS Journal of Computation and Mathematics, vol. 19, pp. 37 - 41, http://dx.doi.org/10.1112/S1461157015000340

Platt DJ; Trudgian TS, 2016, 'On the first sign change of θ(x)-x', Mathematics of Computation, vol. 85, pp. 1539 - 1547, http://dx.doi.org/10.1090/mcom/3021

Platt DJ; Trudgian TS, 2016, 'Diophantine quintuples containing triples of the first kind', Periodica Mathematica Hungarica, vol. 72, pp. 235 - 242, http://dx.doi.org/10.1007/s10998-016-0127-2

Platt DJ; Trudgian TS, 2015, 'Linnik's approximation to Goldbach's conjecture, and other problems', Journal of Number Theory, vol. 153, pp. 54 - 62, http://dx.doi.org/10.1016/j.jnt.2015.01.008

Trudgian TS, 2015, 'An improved upper bound for the error in the zero-counting formulae for Dirichlet L-functions and Dedekind zeta-functions', Mathematics of Computation, vol. 84, pp. 1439 - 1450

Trudgian TS, 2015, 'A short extension of two of spira's results', Journal of Mathematical Inequalities, vol. 9, pp. 795 - 798, http://dx.doi.org/10.7153/jmi-09-65

Akbary A; Trudgian TS, 2015, 'A log-free zero-density estimate and small gaps in coefficients of L-functions', International Mathematics Research Notices, vol. 2015, pp. 4242 - 4268, http://dx.doi.org/10.1093/imrn/rnu065

Trudgian T, 2015, 'The sum of the unitary divisor function', Publications de l'Institut Mathematique, vol. 97, pp. 175 - 180, http://dx.doi.org/10.2298/PIM140617001T

Saouter Y; Trudgian T; Demichel P, 2015, 'A still sharper region where π(x) - li(x) is positive', Mathematics of Computation, vol. 84, pp. 2433 - 2446, http://dx.doi.org/10.1090/S0025-5718-2015-02930-5

Trudgian T, 2015, 'Explicit bounds on the logarithmic derivative and the reciprocal of the Riemann zeta-function', Functiones et Approximatio, Commentarii Mathematici, vol. 52, pp. 253 - 261, http://dx.doi.org/10.7169/facm/2015.52.2.5

Cohen SD; Silva TO; Trudgian T, 2015, 'On consecutive primitive elements in a finite field', Bulletin of the London Mathematical Society, vol. 47, pp. 418 - 426, http://dx.doi.org/10.1112/blms/bdv018

Trudgian T, 2015, 'Bounds on the number of Diophantine quintuples', Journal of Number Theory, vol. 157, pp. 233 - 249, http://dx.doi.org/10.1016/j.jnt.2015.05.004

Cohen SD; Silva TOE; Trudgian T, 2015, 'A proof of the conjecture of Cohen and Mullen on sums of primitive roots', Mathematics of Computation, vol. 84, pp. 2979 - 2986, http://dx.doi.org/10.1090/mcom/2950

Broughan K; Trudgian TS, 2015, 'Robin's inequality for 11-free integers', Integers: electronic journal of combinatorial number theory, vol. 15

Platt DJ; Trudgian TS, 2015, 'An improved explicit bound on', Journal of Number Theory, vol. 147, pp. 842 - 851, http://dx.doi.org/10.1016/j.jnt.2014.08.019

Best DG; Trudgian TS, 2015, 'Linear relations of zeroes of the zeta-function', Mathematics of Computation, vol. 84, pp. 2047 - 2058

Mossinghoff MJ; Trudgian TS, 2015, 'Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function', Journal of Number Theory, vol. 157, pp. 329 - 349, http://dx.doi.org/10.1016/j.jnt.2015.05.010

Trudgian TS, 2014, 'An improved upper bound for the argument of the Riemann zeta-function on the critical line II', Journal of Number Theory, vol. 134, pp. 280 - 292, http://dx.doi.org/10.1016/j.jnt.2013.07.017

Trudgian T, 2014, 'A new upper bound for ζ(1+ it)', Bulletin of the Australian Mathematical Society, vol. 89, pp. 259 - 264, http://dx.doi.org/10.1017/S0004972713000415

Trudgian TS, 2014, 'There are no socialist primes less than 10^9', Integers: electronic journal of combinatorial number theory, vol. 14

Trudgian T, 2012, 'An improved upper bound for the argument of the riemann zeta-function on the critical line', Mathematics of Computation, vol. 81, pp. 1053 - 1061, http://dx.doi.org/10.1090/S0025-5718-2011-02537-8

Trudgian TS, 2012, 'On Selberg's method and multiplicities of the zeroes of the Riemann zeta-function', Commentarii Mathematici Universitatis Sancti Pauli, vol. 60, pp. 227 - 229

Mossinghoff MJ; Trudgian TS, 2012, 'Between the problems of Pólya and Turán', Journal of the Australian Mathematical Society, vol. 93, pp. 157 - 171, http://dx.doi.org/10.1017/S1446788712000201

Trudgian TS, 2011, 'On the success and failure of Gram's Law and the Rosser Rule', Acta Arithmetica, vol. 148, pp. 225 - 256, http://dx.doi.org/10.4064/aa148-3-2

Trudgian T, 2011, 'Improvements to Turing's method', Mathematics of Computation, vol. 80, pp. 2259 - 2279, http://dx.doi.org/10.1090/S0025-5718-2011-02470-1

Trudgian TS, 2010, 'On a conjecture of Shanks', Journal of Number Theory, vol. 130, pp. 2635 - 2638, http://dx.doi.org/10.1016/j.jnt.2010.04.010