61 citations · 445 across the 59 of their papers we have counts for
60 papers
Jonathan Michael Borwein 1951-2016: Life and Legacy
Richard P. Brent
Jonathan M. Borwein (1951-2016) was a prolific mathematician whose career spanned several countries (UK, Canada, USA, Australia) and whose many interests included analysis, optimis…
Some instructive mathematical errors
Richard P. Brent
We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Mapl…
On some results of Agelas concerning the GRH and of Vassilev-Missana concerning the prime zeta function
Richard P. Brent
A recent paper by Agélas [Generalized Riemann Hypothesis, 2019, hal-00747680v3] claims to prove the Generalized Riemann Hypothesis (GRH) and, as a special case, the Riemann Hypothe…
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 , where is a given function, and ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval. We…
A harmonic sum over nontrivial zeros of the Riemann zeta-function
Richard P. Brent, David J. Platt, Timothy S. Trudgian
We consider the sum , where ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in an interval , and consider the behaviour of the sum a…
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, , where This proves (and improves on) a claim by Pintz fro…