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The Australian National University

Dr Timothy Trudgian

BSc (Hons) ANU 2005, DPhil Oxf 2010
ARC Early Career Research Fellow
ANU College of Physical and Mathematical Sciences
T: + 61 2 6125 3620

Areas of expertise

  • Algebra And Number Theory 010101

Research interests

Analytic Number Theory


I graduated from the Australian National University in 2005, and received a General Sir John Monash Award to study overseas. In early 2010 I was awarded my DPhil from the University of Oxford, having studied under Prof. D.R. Heath-Brown.

I once took 6/24 in a college cricket match bowling an optimistic variety of medium-pace. I rather suspect that the opposition reversed their batting order.

During 2009-2010 I was a Lecturer in Mathematics at Merton College, Oxford. During 2010-2012 I was a postdoctoral research fellow at the University of Lethbridge.

Researcher's projects

  1. Sign changes in some arithmetic functions (with Amir Akbary, Lethbridge)
  2. The first sign change in Mertens' formula (with Yannick Saouter, CNRS and Patrick Demichel, Hewlett-Packard France)
  3. Quadratic polynomials over primitive roots (with Stephen Cohen, Glasgow, and Tom\'{a}s Oliveira e Silva, Aveiro)
  4. Diophantine quintuples (with Dave Platt, Bristol)

Available student projects

The following is a brief list of some honours and undergraduate projects. Please email me for more information.

Some general topics that provide an introduction to analytic number theory are

  1. The theory of the Riemann zeta-function
  2. Waring's problem
  3. Computational searches for specific primes

Some specific topics are

  1. Turan's power sum method
  2. The failure of the Mertens conjecture
  3. Explicit zero-free regions of the zeta-function and other L-functions
  4. Skewes' Number for Mertens' theorem

Current student projects

  • Adrian Dudek, PhD Student, Explicit estimates in number theory, commenced November 2012
  • Stijn Hanson, PhD Student, Almost-prime k-tuples, commenced November 2014
  • Jeffrey Lay, PhD Student, Oscillation Theorems, commenced November 2014


Past student projects

  • Benedict Morrissey, Summer Research Scholar, Zero-density theorems for the Riemann zeta-function, 2012-2013
  • Shuhui He, Summer Research Scholar, Exploring exponent pairs, 2012-2013
  • Eloise Hamilton, Summer Research Scholar, Explicit bounds on the nth prime number, 2013-2014
  • Nam Ho, Summer Research Scholar, Elliptic curves and triangle problems, 2013-2014
  • Jeffrey Lay, Honours Student, On the multiplicities of the zeroes of the Riemann zeta-function, 2013-2014
  • Kirsty Chalker, Summer Research Scholar, Zeroes of the Riemann zeta-function on the critical line, 2014-2015
  • Owen Hearder, Summer Research Scholar, Explicit divisor sums, 2014-2015
  • Kam-hung Yau, Summer Research Scholar, Gaps between zeroes of the Riemann zeta-function, 2014-2015
  • Madeleine Kyng, Summer Research Scholar, Consecutive primitive roots modulo a prime, 2015-2016
  • Mitchell Chiew, Summer Research Scholar, Square-free numbers in short intervals, 2015-2016
  • Jakob Vtv, Summer Research Scholar, Consecutive square-free numbers, 2015-2016


Projects and Grants

Grants are drawn from ARIES. To add Projects or Grants please contact your College Research Office.

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Updated:  06 December 2016 / Responsible Officer:  Director (Research Services Division) / Page Contact:  Researchers