359 citations
- Australian National UniversityAU211 papers
- Chongqing UniversityCN12 papers
- International Centre for Radio Astronomy ResearchAU12 papers
- Curtin UniversityAU11 papers
- The University of MelbourneAU9 papers
- UNSW SydneyAU9 papers
- Centre National de la Recherche ScientifiqueFR8 papers
- La Trobe UniversityAU7 papers
- The University of SydneyAU7 papers
- University of CambridgeGB7 papers
- University of WollongongAU7 papers
- Max Planck Institute for AstrophysicsDE6 papers
6 papers · 2 filters
Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function
Michael J. Mossinghoff, Timothy S. Trudgian
We prove that the Riemann zeta-function has no zeros in the region for . This represents the largest known zero-free region w…
A proof of the conjecture of Cohen and Mullen on sums of primitive roots
Stephen D. Cohen, Tomás Oliveira e Silva, Tim Trudgian
We prove that for all , every non-zero element in the finite field can be written as a linear combination of two primitive roots of . This re…
Almost-Ramanujan Graphs and Prime Gaps
Adrian Dudek
The method of Murty and Cioabă shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler constructio…
On the Riemann Hypothesis and the Difference Between Primes
Adrian Dudek
We prove some results concerning the distribution of primes on the Riemann hypothesis. First, we prove the explicit result that there exists a prime in the interval $(x-\frac{4}π \…
An improved explicit bound on
Dave Platt, Tim Trudgian
This article proves the bound for , which improves on a result by Cheng and Graham. We also show that $|ζ(\frac{1…
Updating the error term in the prime number theorem
Tim Trudgian
An improved estimate is given for , where . Three applications are given: the first to arithmetic progressions that have points in common,…