61 citations · 445 across the 59 of their papers we have counts for
6 papers · 1 filter
A note on Pólya's observation concerning Liouville's function
Richard P. Brent, Jan van de Lune
We show that a certain weighted mean of the Liouville function lambda(n) is negative. In this sense, we can say that the Liouville function is negative "on average".
Maximal determinants and saturated D-optimal designs of orders 19 and 37
Richard P. Brent, William Orrick, Judy-anne Osborn +1
A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known…
A note on the real part of the Riemann zeta-function
Juan Arias de Reyna, Richard P. Brent, Jan van de Lune
We consider the real part of the Riemann zeta-function in the half-plane . We show how to compute accurately the constant which…
Finding D-optimal designs by randomised decomposition and switching
Richard P. Brent
The Hadamard maximal determinant (maxdet) problem is to find the maximum determinant D(n) of a square {+1, -1} matrix of given order n. Such a matrix with maximum determinant is ca…
Fast computation of Bernoulli, Tangent and Secant numbers
Richard P. Brent, David Harvey
We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such num…
High-Performance Pseudo-Random Number Generation on Graphics Processing Units
Nimalan Nandapalan, Richard P. Brent, Lawrence M. Murray +1
This work considers the deployment of pseudo-random number generators (PRNGs) on graphics processing units (GPUs), developing an approach based on the xorgens generator to rapidly…