By Professor Timothy Trudgian

Journal articles

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

Platt DJ; Trudgian TS, 2015, 'An improved explicit bound on', Journal of Number Theory, 147, pp. 842 - 851, http://dx.doi.org/10.1016/j.jnt.2014.08.019

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, http://dx.doi.org/10.1093/imrn/rnu065

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, http://dx.doi.org/10.1090/mcom/2950

Trudgian TS, 2015, 'A short extension of two of spira's results', Journal of Mathematical Inequalities, 9, pp. 795 - 798, http://dx.doi.org/10.7153/jmi-09-65

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, http://dx.doi.org/10.1090/S0025-5718-2015-02930-5

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, http://dx.doi.org/10.1090/s0025-5718-2014-02898-6

Best DG; Trudgian TS, 2015, 'Linear relations of zeroes of the zeta-function', Mathematics of Computation, 84, pp. 2047 - 2058, http://dx.doi.org/10.1090/s0025-5718-2014-02916-5

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, http://dx.doi.org/10.1112/blms/bdv018

Trudgian T, 2015, 'The sum of the unitary divisor function', Publications de l'Institut Mathematique, 97, pp. 175 - 180, http://dx.doi.org/10.2298/PIM140617001T

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

Trudgian T, 2014, 'A new upper bound for ζ(1+ it)', Bulletin of the Australian Mathematical Society, 89, pp. 259 - 264, http://dx.doi.org/10.1017/S0004972713000415

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, 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, 14

Mossinghoff MJ; Trudgian TS, 2012, 'Between the problems of Pólya and Turán', Journal of the Australian Mathematical Society, 93, pp. 157 - 171, http://dx.doi.org/10.1017/S1446788712000201

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, http://dx.doi.org/10.1090/S0025-5718-2011-02537-8

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

Trudgian T, 2011, 'Improvements to Turing’s method', Mathematics of Computation, 80, pp. 2259 - 2259, http://dx.doi.org/10.1090/S0025-5718-2011-02470-1

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

Trudgian TS, 2010, 'On a conjecture of Shanks', Journal of Number Theory, 130, pp. 2635 - 2638, http://dx.doi.org/10.1016/j.jnt.2010.04.010

Conference Papers

Platt D; Trudgian T, 2020, 'Improved bounds on Brun’s constant', in Springer Proceedings in Mathematics and Statistics, pp. 395 - 406, http://dx.doi.org/10.1007/978-3-030-36568-4_25

Preprints

Mossinghoff MJ; Trudgian TS; Yang A, 2022, Explicit zero-free regions for the Riemann zeta-function, http://dx.doi.org/10.48550/arxiv.2212.06867

Bellotti C; Keller TM; Trudgian TS, 2022, New bounds for numbers of primes in element orders of finite groups, http://dx.doi.org/10.48550/arxiv.2211.05837

Goldston DA; Trudgian TS; Turnage-Butterbaugh CL, 2022, On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function, http://dx.doi.org/10.48550/arxiv.2201.10676

Martin G; Mossinghoff MJ; Trudgian TS, 2021, Fake Mu's, http://dx.doi.org/10.48550/arxiv.2112.05227

Mossinghoff MJ; Starichkova VV; Trudgian TS, 2021, Explicit lower bounds on $|L(1, χ)|$, http://arxiv.org/abs/2107.09230v1

Booker AR; Hathi S; Mossinghoff MJ; Trudgian TS, 2021, Wolstenholme and Vandiver primes, http://dx.doi.org/10.48550/arxiv.2101.11157

Languasco A; Trudgian TS, 2020, Uniform effective estimates for $\vert L(1,\chi)\vert$, http://dx.doi.org/10.48550/arxiv.2011.08348

Simonič A; Trudgian T; Turnage-Butterbaugh CL, 2020, Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function, http://dx.doi.org/10.48550/arxiv.2010.10675

Brent RP; Platt DJ; Trudgian TS, 2020, Accurate estimation of sums over zeros of the Riemann zeta-function, http://dx.doi.org/10.48550/arxiv.2009.13791

Brent RP; Platt DJ; Trudgian TS, 2020, A harmonic sum over nontrivial zeros of the Riemann zeta-function, http://dx.doi.org/10.48550/arxiv.2009.05251

Brent RP; Platt DJ; Trudgian TS, 2020, The mean square of the error term in the prime number theorem, http://dx.doi.org/10.48550/arxiv.2008.06140

Mossinghoff MJ; Trudgian TS, 2020, Oscillations in weighted arithmetic sums, http://dx.doi.org/10.48550/arxiv.2007.14537

Mossinghoff MJ; Trudgian TS, 2020, The size of oscillations in the Goldbach conjecture, http://dx.doi.org/10.48550/arxiv.2006.14742

Mossinghoff MJ; Trudgian TS, 2019, A tale of two omegas, http://dx.doi.org/10.48550/arxiv.1906.02847

Mossinghoff MJ; Trudgian TS, 2014, Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function, http://dx.doi.org/10.48550/arxiv.1410.3926

Akbary A; Trudgian TS, 2013, A log-free zero-density estimate and small gaps in coefficients of $L$-functions, http://dx.doi.org/10.48550/arxiv.1312.5820

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