R. Brent

activity

20072021

most citedOn the stability of the Bareiss and related Toeplitz factorization algorithms

61 citations · 445 across the 59 of their papers we have counts for

collaborators

Showing 2020Show all

3 papers · 1 filter

math.NT2020★ 20 cited

Accurate estimation of sums over zeros of the Riemann zeta-function

Richard P. Brent, David J. Platt, Timothy S. Trudgian

We consider sums of the form $\sum ϕ (γ)$ , where $ϕ$ is a given function, and $γ$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval. We…

math.NT2020★ 2 cited

A harmonic sum over nontrivial zeros of the Riemann zeta-function

Richard P. Brent, David J. Platt, Timothy S. Trudgian

We consider the sum $\sum 1/ γ$ , where $γ$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in an interval $(0, T]$ , and consider the behaviour of the sum a…

math.NT2020

The mean square of the error term in the prime number theorem

Richard P. Brent, David J. Platt, Timothy S. Trudgian

We show that, on the Riemann hypothesis, $lim sup_{X \to \infty} I (X) / X^{2} \leq 0.8603$ , where $I (X) = \int_{X}^{2 X} (ψ (x) - x)^{2} d x .$ This proves (and improves on) a claim by Pintz fro…