Timothy S. Trudgian

most citedUpdating the error term in the prime number theorem

6 citations · 9 across the 2 of their papers we have counts for

collaborators

2 papers

math.NT2014★ 3 cited

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 $ζ (σ + i t)$ has no zeros in the region $σ \geq 1 - 1/ (5.573412 lo g ∣ t ∣)$ for $∣ t ∣ \geq 2$ . This represents the largest known zero-free region w…

math.NT2014★ 6 cited

Updating the error term in the prime number theorem

Tim Trudgian

An improved estimate is given for $∣ θ (x) - x ∣$ , where $θ (x) = \sum_{p \leq x} lo g p$ . Three applications are given: the first to arithmetic progressions that have points in common,…