Richard P. Brent

Richard Peirce Brent
Nationality	Australian
Alma mater	Stanford University
Awards	Hannan Medal (2005)
Scientific career
Fields	Mathematics, computer science
Institutions	Australian National University
Doctoral advisors	Gene H. Golub George Forsythe

Richard Peirce Brent is an Australian

.

In 1973, he published a

In 1975 he and

Salamin–Brent algorithm

, used in high-precision calculation of ${\displaystyle \pi }$. 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 ${\displaystyle \pi }$ (apart from a small constant factor) using the

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.^[4]

In 1980 he and Nobel laureate

${\displaystyle \gamma }$ using Bessel functions, and showed that ${\displaystyle \gamma }$ can not have a simple rational form p/q (where p and q are integers) unless q is extremely large (greater than 10¹⁵⁰⁰⁰).^[5]

In 1980 he and

algorithm.

In 2002, Brent, Samuli Larvala and

(2):

${\displaystyle x^{6972593}+x^{3037958}+1.}$

The degree 6972593 is the exponent of a Mersenne prime.^[8]

In 2009 and 2016, Brent and Paul Zimmermann discovered some even larger primitive trinomials, for example:

${\displaystyle x^{43112609}+x^{3569337}+1.}$

The degree

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

.

See also

• Brent–Kung adder

References

External links

• Richard Brent's home page
• Richard P. Brent at the Mathematics Genealogy Project