Dr Timothy Trudgian
Areas of expertise
- Algebra And Number Theory 010101
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.
- An explicit sub-convexity estimate for the zeta-function (with Dave Platt, Bristol)
- A further improvement on S(t)
- A log-free zero-density theorem for a class of L-functions (with Amir Akbary, Lethbridge)
- An explicit bound on 1/|\zeta(\sigma + it)| for \sigma near 1
- The Linnik--Golbach problem (with Dave Platt, Bristol)
- The first sign change in Mertens' formula (with Yannick Saouter, CNRS and Patrick Demichel, Hewlett-Packard France)
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
- The theory of the Riemann zeta-function
- Waring's problem
- Computational searches for specific primes
Some specific topics are
- Turan's power sum method
- The failure of the Mertens conjecture
- Explicit zero-free regions of the zeta-function and other L-functions
- Skewes' Number for Mertens' theorem
- Adrian Dudek, PhD Student, Consequences of numerical verification of the Riemann hypothesis to large heights, commenced November 2012
- Jeffrey Lay, Honours Student, Multiplicities of the zeroes of the Riemann zeta-function, commenced July 2013
- 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