5 papers
A conjecture of Glasby, Praeger, and Unger on permutations of
Chiara Bellotti, Tim Trudgian
We prove a conjecture of Glasby, Praeger, and Unger concerning the symmetric group . Let denote the proportion of elements of that are pre--cycles for som…
An update on the Linnik--Goldbach problem
Daniel R. Johnston, Tim Trudgian
We consider the Linnik--Goldbach problem of writing all large even integers as the sum of two primes and a fixed number of powers of 2. We show that, under the generalised Riemann…
Zero-free regions inspired by work of Heath-Brown
Chiara Bellotti, Tim Trudgian, Andrew Yang
We prove a new explicit zero-free region for the Riemann zeta-function, drawing substantially on Heath-Brown's seminal work on Linnik's constant. Using these ideas we are able to p…
New bounds for numbers of primes in element orders of finite groups
Chiara Bellotti, Thomas Michael Keller, Timothy S. Trudgian
Let denote the maximal number of different primes that may occur in the order of a finite solvable group , all elements of which have orders divisible by at most dist…
The error term in the prime number theorem
Dave Platt, Tim Trudgian
We make explicit a theorem of Pintz concerning the error term in the prime number theorem. This gives an improved version of the prime number theorem with error term roughly square…