Richard Peirce Brent (born 20 April 1946,
Melbourne) is an Australian mathematician
and computer scientist.
He is an emeritus professor at the Australian
National University and a conjoint professor
at the University of Newcastle (Australia).
From March 2005 to March 2010 he was a Federation
Fellow at the Australian National University.
His research interests include number theory
(in particular factorisation), random number
generators, computer architecture, and analysis
of algorithms.
In 1973, he published a root-finding algorithm
(an algorithm for solving equations numerically)
which is now known as Brent's method.In 1975
he and Eugene Salamin independently conceived
the Salamin–Brent algorithm, used in high-precision
calculation of
π
{\displaystyle \pi }
. At the same time, he showed that all the
elementary functions (such as log(x), sin(x)
etc.) can be evaluated to high precision in
the same time as
π
{\displaystyle \pi }
(apart from a small constant factor) using
the arithmetic-geometric mean of Carl Friedrich
Gauss.In 1979 he showed that the first 75
million complex zeros of the Riemann zeta
function lie on the critical line, providing
some experimental evidence for the Riemann
hypothesis.In 1980 he and Nobel laureate Edwin
McMillan found a new algorithm for high-precision
computation of the Euler–Mascheroni constant
γ
{\displaystyle \gamma }
using Bessel functions, and showed that
γ
{\displaystyle \gamma }
can not have a simple rational form p/q (where
p and q are integers) unless q is extremely
large (greater than 1015000).In 1980 he and
John Pollard factored the eighth Fermat number
using a variant of the Pollard rho algorithm.
He later factored the tenth and eleventh Fermat
numbers using Lenstra's elliptic curve factorisation
algorithm.
In 2002, Brent, Samuli Larvala and Paul Zimmermann
discovered a very large primitive trinomial
over GF(2):
x
6972593
+
x
3037958
+
1.
{\displaystyle x^{6972593}+x^{3037958}+1.}
The degree 6972593 is the exponent of a Mersenne
prime.In 2009 and 2016, Brent and Paul Zimmermann
discovered some even larger primitive trinomials,
for example:
x
43112609
+
x
3569337
+
1.
{\displaystyle x^{43112609}+x^{3569337}+1.}
The degree 43112609 is again the exponent
of a Mersenne prime.In 2011, Brent and Paul
Zimmermann published Modern Computer Arithmetic
(Cambridge University Press), a book about
algorithms for performing arithmetic, and
their implementation on modern computers.
Brent is a Fellow of the Association for Computing
Machinery, the IEEE, SIAM and the Australian
Academy of Science.
In 2005, he was awarded the Hannan Medal by
the Australian Academy of Science.
In 2014, he was awarded the Moyal Medal by
Macquarie University.
== See also ==
Brent–Kung adder
