## 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

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, 10.1090/mcom/3357

Munsch M; Trudgian T, 2018, 'Square-full primitive roots', *International Journal of Number Theory*, vol. 14, pp. 1013 - 1021, 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, 10.1016/j.ffa.2018.02.009

Platt D; Trudgian T, 2018, 'Fujii's development on Chebyshev's conjecture', *International Journal of Number Theory*, pp. 1 - 6, 10.1142/S1793042119500337

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, 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, 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, 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, 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, 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, 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, 10.1216/RMJ-2016-46-1-325

Cipu M; Trudgian T, 2016, 'Searching for Diophantine quintuples', *Acta Arithmetica*, vol. 173, pp. 365 - 382, 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, 10.4064/aa8109-12-2015

Trudgian T, 2016, 'Updating the error term in the prime number theorem', *Ramanujan Journal*, vol. 39, pp. 225 - 234, 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, 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, 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, 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, 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, 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, 10.1090/mcom/2950

Trudgian T, 2015, 'Bounds on the number of Diophantine quintuples', *Journal of Number Theory*, vol. 157, pp. 233 - 249, 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, 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, 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, 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, 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, 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, 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, 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, 10.1090/S0025-5718-2011-02537-8

Trudgian T, 2011, 'Improvements to Turing's method', *Mathematics of Computation*, vol. 80, pp. 2259 - 2279, 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, 10.4064/aa148-3-2

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