Dr Timothy Trudgian

t.trudgian@adfa.edu.au
+61 2 626 88021

LOCATION

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

  • ABOUT
  • PUBLICATIONS

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

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

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

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

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

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

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

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

Trudgian T; Wang Q, 2017, 'The T4and G4constructions of Costas arrays', Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 100, pp. 217 - 221

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

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, 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, '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

McGown K; Treviño E; Trudgian T, 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

Trudgian T, 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

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

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

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

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, 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

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

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

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

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

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

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

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 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, '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

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, 'The sum of the unitary divisor function', Publications de l'Institut Mathematique, vol. 97, pp. 175 - 180, http://dx.doi.org/10.2298/PIM140617001T

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

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

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, 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

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 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 T, 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 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