599 citations
- UNSW SydneyAU122 papers
- Australian Defence Force AcademyAU85 papers
- University of CanberraAU55 papers
- Australian National UniversityAU52 papers
- Centre for Quantum Computation and Communication TechnologyAU28 papers
- Chinese Academy of SciencesCN16 papers
- The University of TokyoJP13 papers
- Academy of Mathematics and Systems ScienceCN12 papers
- Centre National de la Recherche ScientifiqueFR10 papers
- Nanjing UniversityCN10 papers
- Princeton UniversityUS10 papers
- Australian Research CouncilAU9 papers
13 papers · 1 filter
On the number of integral ideals in a number field
Ethan Simpson Lee
We update Sunley's explicit estimate for the ideal-counting function, which is the number of integral ideals of bounded norm in a number field.
Primes between consecutive powers
Michaela Cully-Hugill
This paper updates the explicit interval estimate for primes between consecutive powers. It is shown that there is least one prime between and for all $n\ge…
Explicit Interval Estimates for Prime Numbers
Michaela Cully-Hugill, Ethan S. Lee
Using a smoothing function and recent knowledge on the zeros of the Riemann zeta-function, we compute pairs of such that for all there exists at least one pr…
Uniform effective estimates for
Alessandro Languasco, Timothy S. Trudgian
Let be the Dirichlet -function associated to a non-principal primitive Dirichlet character defined modulo , where . We prove, under the assumption of the…
Unconditional Explicit Mertens' Theorems for Number Fields and Dedekind Zeta Residue Bounds
Stephan Ramon Garcia, Ethan Simpson Lee
We obtain unconditional, effective number-field analogues of the three Mertens' theorems, all with explicit constants and valid for . Our error terms are explicitly bounde…
The Riemann hypothesis is true up to
Dave Platt, Tim Trudgian
We verify numerically, in a rigorous way using interval arithmetic, that the Riemann hypothesis is true up to height . That is, all zeroes of the Riemann zet…