Professor Timothy Trudgian

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 .

Scholarships of $37,500 (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 timothy.trudgian@unsw.edu.au. I particularly encourage female mathematicians to apply.

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

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

Phone

+61 2 5114 5026

E-mail

t.trudgian@adfa.edu.au

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

Book Chapters | 2020

Mossinghoff M; Trudgian T, 2020, 'A tale of two omegas', in , American Mathematical Society, pp. 343 - 364,

Book Chapters | 2017

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 | 2024

Mossinghoff MJ; Trudgian TS; Yang A, 2024, 'Explicit zero-free regions for the Riemann zeta-function', Research in Number Theory, 10,

Journal articles | 2023

Bellotti C; Keller TM; Trudgian TS, 2023, 'New bounds for numbers of primes in element orders of finite groups', Mathematische Nachrichten, 296, pp. 5227 - 5231,

Journal articles | 2023

Goldston DA; Trudgian TS; Turnage-Butterbaugh CL, 2023, 'On the Montgomery–Odlyzko method regarding gaps between zeros of the zeta-function', Journal of Mathematical Analysis and Applications, 527,

Journal articles | 2023

Johnston DR; Ramaré O; Trudgian T, 2023, 'An explicit upper bound for L(1 , χ) when χ is quadratic', Research in Number Theory, 9,

Journal articles | 2023

Martin G; Mossinghoff MJ; Trudgian TS, 2023, 'Fake mu’s', Proceedings of the American Mathematical Society, 151, pp. 3229 - 3244,

Journal articles | 2022

Booker AR; Cohen SD; Leong N; Trudgian T, 2022, 'PRIMITIVE ELEMENT PAIRS with A PRESCRIBED TRACE in the CUBIC EXTENSION of A FINITE FIELD', Bulletin of the Australian Mathematical Society, 106, pp. 458 - 462,

Journal articles | 2022

Booker AR; Cohen SD; Leong N; Trudgian T, 2022, 'Primitive elements with prescribed traces', Finite Fields and their Applications, 84,

Journal articles | 2022

Booker AR; Hathi S; Mossinghoff MJ; Trudgian TS, 2022, 'Wolstenholme and Vandiver primes', Ramanujan Journal, 58, pp. 913 - 941,

Journal articles | 2022

Brent RP; Platt DJ; Trudgian TS, 2022, 'The mean square of the error term in the prime number theorem', Journal of Number Theory, 238, pp. 740 - 762,

Journal articles | 2022

Jarso T; Trudgian T, 2022, 'FOUR CONSECUTIVE PRIMITIVE ELEMENTS IN A FINITE FIELD', Mathematics of Computation, 91, pp. 1521 - 1532,

Journal articles | 2022

Languasco A; Trudgian TS, 2022, 'Uniform effective estimates for', Journal of Number Theory, 236, pp. 245 - 260,

Journal articles | 2022

Morrill T; Platt D; Trudgian T, 2022, 'Sign changes in the prime number theorem', Ramanujan Journal, 57, pp. 165 - 173,

Journal articles | 2022

Mossinghoff MJ; Starichkova VV; Trudgian TS, 2022, 'Explicit lower bounds on', Journal of Number Theory, 240, pp. 641 - 655,

Journal articles | 2022

Mossinghoff MJ; Trudgian TS, 2022, 'Oscillations in the Goldbach conjecture', Journal de Theorie des Nombres de Bordeaux, 34, pp. 395 - 307,

Journal articles | 2022

Simonič A; TRUDGIAN TS; TURNAGE-BUTTERBAUGH CL, 2022, 'SOME EXPLICIT AND UNCONDITIONAL RESULTS ON GAPS BETWEEN ZEROES OF THE RIEMANN ZETA-FUNCTION', Transactions of the American Mathematical Society, 375, pp. 3239 - 3265,

Journal articles | 2021

Brent RP; Platt DJ; Trudgian TS, 2021, 'A HARMONIC SUM over NONTRIVIAL ZEROS of the RIEMANN ZETA-FUNCTION', Bulletin of the Australian Mathematical Society, 104, pp. 59 - 65,

Journal articles | 2021

Brent RP; Platt DJ; Trudgian TS, 2021, 'Accurate estimation of sums over zeros of the riemann zeta-function', Mathematics of Computation, 90, pp. 2923 - 2935,

Journal articles | 2021

Cully-Hugill M; Trudgian T, 2021, 'Two explicit divisor sums', Ramanujan Journal, 56, pp. 141 - 149,

Journal articles | 2021

MOSSINGHOFF MJ; SILVA TOE; TRUDGIAN TS, 2021, 'the Distribution of K-Free Numbers', Mathematics of Computation, 90, pp. 907 - 929,

Journal articles | 2021

Mossinghoff MJ; Trudgian TS, 2021, 'Oscillations in weighted arithmetic sums', International Journal of Number Theory, 17, pp. 1697 - 1716,

Journal articles | 2021

PLATT DJ; TRUDGIAN TS, 2021, 'the Error Term in the Prime Number Theorem', Mathematics of Computation, 90, pp. 871 - 881,

Journal articles | 2021

Platt D; Trudgian T, 2021, 'The Riemann hypothesis is true up to 3·1012', Bulletin of the London Mathematical Society, 53, pp. 792 - 797,

Journal articles | 2020

Kerr B; McGown KJ; Trudgian T, 2020, 'The least primitive root modulo p²', Journal of Number Theory, 215, pp. 20 - 27,

Journal articles | 2020

Kobayashi M; Trudgian T, 2020, 'On integers n for which σ(2n + 1)≥σ(2n)', Journal of Number Theory, 215, pp. 138 - 148,

Journal articles | 2020

McGown KJ; Trudgian T, 2020, 'Explicit upper bounds on the least primitive root', Proceedings of the American Mathematical Society, 148, pp. 1049 - 1061,

Journal articles | 2019

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, 88, pp. 931 - 947,

Journal articles | 2019

Cohen SD; Trudgian T, 2019, 'Lehmer numbers and primitive roots modulo a prime', Journal of Number Theory, 203, pp. 68 - 79,

Journal articles | 2019

Morrill T; Trudgian T, 2019, 'An elementary bound on Siegel zeroes', Journal of Number Theory,

Journal articles | 2019

Platt D; Trudgian T, 2019, 'Fujii's development on Chebyshev's conjecture', International Journal of Number Theory, 15, pp. 639 - 644,

Journal articles | 2018

Booker AR; Cohen SD; Sutherland N; Trudgian T, 2018, 'Primitive values of quadratic polynomials in a finite field', Mathematics of Computation, 88, pp. 1903 - 1912,

Journal articles | 2018

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, 51, pp. 388 - 406,

Journal articles | 2018

Jarso T; Trudgian T, 2018, 'Quadratic non-residues that are not primitive roots', Mathematics of Computation, 88, pp. 1251 - 1260,

Journal articles | 2018

Munsch M; Trudgian T, 2018, 'Square-full primitive roots', International Journal of Number Theory, 14, pp. 1013 - 1021,

Journal articles | 2017

Cohen SD; Trudgian T, 2017, 'On the least square-free primitive root modulo p', Journal of Number Theory, 170, pp. 10 - 16,

Journal articles | 2017

Platt DJ; Trudgian TS, 2017, 'On the sum of two squares and at most two powers of 2', American Mathematical Monthly, 124, pp. 737 - 740,

Journal articles | 2017

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

Journal articles | 2016

Cipu M; Trudgian T, 2016, 'Searching for Diophantine quintuples', Acta Arithmetica, 173, pp. 365 - 382,

Journal articles | 2016

Cohen SD; Oliveira E Silva T; Trudgian T, 2016, 'On Grosswald's conjecture on primitive roots', Acta Arithmetica, 172, pp. 263 - 270,

Journal articles | 2016

McGown K; Trevino E; Trudgian TS, 2016, 'Resolving Grosswald's conjecture on GRH', Functiones et Approximatio Commentarii Mathematici, 55, pp. 215 - 225

Journal articles | 2016

Platt DJ; Trudgian TS, 2016, 'Diophantine quintuples containing triples of the first kind', Periodica Mathematica Hungarica, 72, pp. 235 - 242,

Journal articles | 2016

Platt DJ; Trudgian TS, 2016, 'On the first sign change of θ(x)-x', Mathematics of Computation, 85, pp. 1539 - 1547,

Journal articles | 2016

Platt DJ; Trudgian TS, 2016, 'Zeroes of partial sums of the zeta-function', LMS Journal of Computation and Mathematics, 19, pp. 37 - 41,

Journal articles | 2016

Trudgian T, 2016, 'Updating the error term in the prime number theorem', Ramanujan Journal, 39, pp. 225 - 234,

Journal articles | 2016

Trudgian TS, 2016, 'Improvements to Turing's Method II', Rocky Mountain Journal of Mathematics, 46, pp. 325 - 332

Journal articles | 2015

Akbary A; Trudgian TS, 2015, 'A log-free zero-density estimate and small gaps in coefficients of L-functions', International Mathematics Research Notices, 2015, pp. 4242 - 4268,

Journal articles | 2015

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

Journal articles | 2015

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

Journal articles | 2015

Cohen SD; Silva TO; Trudgian T, 2015, 'On consecutive primitive elements in a finite field', Bulletin of the London Mathematical Society, 47, pp. 418 - 426,

Journal articles | 2015

Cohen SD; Silva TOE; Trudgian T, 2015, 'A proof of the conjecture of Cohen and Mullen on sums of primitive roots', Mathematics of Computation, 84, pp. 2979 - 2986,

Journal articles | 2015

Mossinghoff MJ; Trudgian TS, 2015, 'Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function', Journal of Number Theory, 157, pp. 329 - 349,

Journal articles | 2015

Platt DJ; Trudgian TS, 2015, 'An improved explicit bound on', Journal of Number Theory, 147, pp. 842 - 851,

Journal articles | 2015

Platt DJ; Trudgian TS, 2015, 'Linnik's approximation to Goldbach's conjecture, and other problems', Journal of Number Theory, 153, pp. 54 - 62,

Journal articles | 2015

Saouter Y; Trudgian T; Demichel P, 2015, 'A still sharper region where π(x) - li(x) is positive', Mathematics of Computation, 84, pp. 2433 - 2446,

Journal articles | 2015

Trudgian T, 2015, 'Bounds on the number of Diophantine quintuples', Journal of Number Theory, 157, pp. 233 - 249,

Journal articles | 2015

Trudgian T, 2015, 'Explicit bounds on the logarithmic derivative and the reciprocal of the Riemann zeta-function', Functiones et Approximatio, Commentarii Mathematici, 52, pp. 253 - 261,

Journal articles | 2015

Trudgian T, 2015, 'The sum of the unitary divisor function', Publications de l'Institut Mathematique, 97, pp. 175 - 180,

Journal articles | 2015

Trudgian TS, 2015, 'A short extension of two of spira's results', Journal of Mathematical Inequalities, 9, pp. 795 - 798,

Journal articles | 2015

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, 84, pp. 1439 - 1450,

Journal articles | 2014

Trudgian T, 2014, 'A new upper bound for ζ(1+ it)', Bulletin of the Australian Mathematical Society, 89, pp. 259 - 264,

Journal articles | 2014

Trudgian TS, 2014, 'An improved upper bound for the argument of the Riemann zeta-function on the critical line II', Journal of Number Theory, 134, pp. 280 - 292,

Journal articles | 2014

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

Journal articles | 2012

Mossinghoff MJ; Trudgian TS, 2012, 'Between the problems of Pólya and Turán', Journal of the Australian Mathematical Society, 93, pp. 157 - 171,

Journal articles | 2012

Trudgian T, 2012, 'An improved upper bound for the argument of the riemann zeta-function on the critical line', Mathematics of Computation, 81, pp. 1053 - 1061,

Journal articles | 2012

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

Journal articles | 2011

Trudgian T, 2011, 'Improvements to Turing’s method', Mathematics of Computation, 80, pp. 2259 - 2259,

Journal articles | 2011

Trudgian TS, 2011, 'On the success and failure of Gram's Law and the Rosser Rule', Acta Arithmetica, 148, pp. 225 - 256

Journal articles | 2010

Trudgian TS, 2010, 'On a conjecture of Shanks', Journal of Number Theory, 130, pp. 2635 - 2638,
Preprints | 2022

Bellotti C; Keller TM; Trudgian TS, 2022, New bounds for numbers of primes in element orders of finite groups, ,

Preprints | 2022

Goldston DA; Trudgian TS; Turnage-Butterbaugh CL, 2022, On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function, ,

Preprints | 2022

Mossinghoff MJ; Trudgian TS; Yang A, 2022, Explicit zero-free regions for the Riemann zeta-function, ,

Preprints | 2021

Booker AR; Hathi S; Mossinghoff MJ; Trudgian TS, 2021, Wolstenholme and Vandiver primes,

Preprints | 2021

Martin G; Mossinghoff MJ; Trudgian TS, 2021, Fake Mu's,

Preprints | 2021

Mossinghoff MJ; Starichkova VV; Trudgian TS, 2021, Explicit lower bounds on $|L(1, χ)|$, ,

Preprints | 2020

Brent RP; Platt DJ; Trudgian TS, 2020, A harmonic sum over nontrivial zeros of the Riemann zeta-function, ,

Preprints | 2020

Brent RP; Platt DJ; Trudgian TS, 2020, Accurate estimation of sums over zeros of the Riemann zeta-function, ,

Preprints | 2020

Brent RP; Platt DJ; Trudgian TS, 2020, The mean square of the error term in the prime number theorem, ,

Preprints | 2020

Languasco A; Trudgian TS, 2020, Uniform effective estimates for $\vert L(1,\chi)\vert$, ,

Preprints | 2020

Mossinghoff MJ; Trudgian TS, 2020, Oscillations in weighted arithmetic sums, ,

Preprints | 2020

Mossinghoff MJ; Trudgian TS, 2020, The size of oscillations in the Goldbach conjecture, ,

Conference Papers | 2020

Platt D; Trudgian T, 2020, 'Improved bounds on Brun’s constant', in Springer Proceedings in Mathematics and Statistics, pp. 395 - 406,

Preprints | 2020

Simonič A; Trudgian T; Turnage-Butterbaugh CL, 2020, Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function, ,

Preprints | 2019

Mossinghoff MJ; Trudgian TS, 2019, A tale of two omegas, ,

Preprints | 2014

Mossinghoff MJ; Trudgian TS, 2014, Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function, ,

Preprints | 2013

Akbary A; Trudgian TS, 2013, A log-free zero-density estimate and small gaps in coefficients of $L$-functions, ,

DECRA, Australian Research Council, 2012-2015.

Discovery Project, Australian Research Council, 2015-2019 (joint with , Bristol).

Future Fellowship, Australian Research Council, 2016-2020.

Discovery Project, Australian Research Council, 2024-2027

My Research Supervision

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