91成人版抖音
Back to
Professor Timothy Trudgian

Professor Timothy Trudgian

Professor
UNSW Canberra
School of Science

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 91成人版抖音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鈥揙dlyzko method regarding gaps between zeros of the zeta-function', Journal of Mathematical Analysis and Applications, 527,
    Journal articles | 2023
    Johnston DR; Ramar茅 O; Trudgian T, 2023, 'An explicit upper bound for L(1 , 蠂) when 蠂 is quadratic', Research in Number Theory, 9,
    Journal articles | 2023
    Martin G; Mossinghoff MJ; Trudgian TS, 2023, 'Fake mu鈥檚', 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
    Simoni膷 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路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 蟽(2n鈥+鈥1)鈮ハ(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 胃(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 蟺(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 味(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 P贸lya and Tur谩n', 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鈥檚 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 $|L(1, 蠂)|$, ,
    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鈥檚 constant', in Springer Proceedings in Mathematics and Statistics, pp. 395 - 406,
    Preprints | 2020
    Simoni膷 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