By Professor Timothy Trudgian

Book Chapters

Mossinghoff M; Trudgian T, 2020, 'A tale of two omegas', in , American Mathematical Society, pp. 343 - 364, http://dx.doi.org/10.1090/conm/754/15149

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

Mossinghoff MJ; Trudgian TS; Yang A, 2024, 'Explicit zero-free regions for the Riemann zeta-function', Research in Number Theory, 10, http://dx.doi.org/10.1007/s40993-023-00498-y

Johnston DR; Ramaré O; Trudgian T, 2023, 'An explicit upper bound for L(1 , χ) when χ is quadratic', Research in Number Theory, 9, http://dx.doi.org/10.1007/s40993-023-00476-4

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, http://dx.doi.org/10.1016/j.jmaa.2023.127548

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, http://dx.doi.org/10.1002/mana.202200484

Martin G; Mossinghoff MJ; Trudgian TS, 2023, 'Fake mu’s', Proceedings of the American Mathematical Society, 151, pp. 3229 - 3244, http://dx.doi.org/10.1090/proc/16186

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, http://dx.doi.org/10.1017/S0004972722000442

Booker AR; Cohen SD; Leong N; Trudgian T, 2022, 'Primitive elements with prescribed traces', Finite Fields and their Applications, 84, http://dx.doi.org/10.1016/j.ffa.2022.102094

Mossinghoff MJ; Starichkova VV; Trudgian TS, 2022, 'Explicit lower bounds on', Journal of Number Theory, 240, pp. 641 - 655, http://dx.doi.org/10.1016/j.jnt.2021.12.013

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, http://dx.doi.org/10.1016/j.jnt.2021.09.016

Languasco A; Trudgian TS, 2022, 'Uniform effective estimates for', Journal of Number Theory, 236, pp. 245 - 260, http://dx.doi.org/10.1016/j.jnt.2021.07.019

Booker AR; Hathi S; Mossinghoff MJ; Trudgian TS, 2022, 'Wolstenholme and Vandiver primes', Ramanujan Journal, 58, pp. 913 - 941, http://dx.doi.org/10.1007/s11139-021-00438-3

Jarso T; Trudgian T, 2022, 'FOUR CONSECUTIVE PRIMITIVE ELEMENTS IN A FINITE FIELD', Mathematics of Computation, 91, pp. 1521 - 1532, http://dx.doi.org/10.1090/mcom/3716

Mossinghoff MJ; Trudgian TS, 2022, 'Oscillations in the Goldbach conjecture', Journal de Theorie des Nombres de Bordeaux, 34, pp. 395 - 307, http://dx.doi.org/10.5802/jtnb.1202

Morrill T; Platt D; Trudgian T, 2022, 'Sign changes in the prime number theorem', Ramanujan Journal, 57, pp. 165 - 173, http://dx.doi.org/10.1007/s11139-021-00398-8

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, http://dx.doi.org/10.1090/tran/8571

Cully-Hugill M; Trudgian T, 2021, 'Two explicit divisor sums', Ramanujan Journal, 56, pp. 141 - 149, http://dx.doi.org/10.1007/s11139-020-00333-3

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, http://dx.doi.org/10.1017/S0004972720001252

Mossinghoff MJ; Trudgian TS, 2021, 'Oscillations in weighted arithmetic sums', International Journal of Number Theory, 17, pp. 1697 - 1716, http://dx.doi.org/10.1142/S1793042121500561

Platt D; Trudgian T, 2021, 'The Riemann hypothesis is true up to 3·1012', Bulletin of the London Mathematical Society, 53, pp. 792 - 797, http://dx.doi.org/10.1112/blms.12460

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, http://dx.doi.org/10.1090/mcom/3652

MOSSINGHOFF MJ; SILVA TOE; TRUDGIAN TS, 2021, 'the Distribution of K-Free Numbers', Mathematics of Computation, 90, pp. 907 - 929, http://dx.doi.org/10.1090/MCOM/3581

PLATT DJ; TRUDGIAN TS, 2021, 'the Error Term in the Prime Number Theorem', Mathematics of Computation, 90, pp. 871 - 881, http://dx.doi.org/10.1090/MCOM/3583

Kobayashi M; Trudgian T, 2020, 'On integers n for which σ(2n + 1)≥σ(2n)', Journal of Number Theory, 215, pp. 138 - 148, 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, 215, pp. 20 - 27, 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, 148, pp. 1049 - 1061, http://dx.doi.org/10.1090/proc/14800

Cohen SD; Trudgian T, 2019, 'Lehmer numbers and primitive roots modulo a prime', Journal of Number Theory, 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, 15, pp. 639 - 644, http://dx.doi.org/10.1142/S1793042119500337

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, 88, pp. 931 - 947, http://dx.doi.org/10.1090/mcom/3357

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, 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, 51, pp. 388 - 406, http://dx.doi.org/10.1016/j.ffa.2018.02.009

Munsch M; Trudgian T, 2018, 'Square-full primitive roots', International Journal of Number Theory, 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, 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, 124, pp. 737 - 740, http://dx.doi.org/10.4169/amer.math.monthly.124.8.737

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

Cohen SD; Trudgian T, 2017, 'On the least square-free primitive root modulo p', Journal of Number Theory, 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, 72, pp. 235 - 242, http://dx.doi.org/10.1007/s10998-016-0127-2

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

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

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

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

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

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

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

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

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, http://dx.doi.org/10.1016/j.jnt.2015.05.010

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

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, http://dx.doi.org/10.7169/facm/2015.52.2.5

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