4 papers · 1 filter
Zeros of quadratic Dirichlet -functions
Dave Platt, Tim Trudgian
We consider Dirichlet -functions where is a quadratic character to modulus . We show that for even (resp. odd) for all provided that $…
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…