Roger Heath-Brown
Encyclopedia
David Rodney "Roger" Heath-Brown F.R.S. (born 12 October 1952), is a British mathematician
working in the field of analytic number theory
. He was an undergraduate and graduate student of Trinity College, Cambridge
; his research supervisor was Alan Baker. In 1979 he moved to the University of Oxford
, where since 1999 he has held a professorship in pure mathematics
.
Heath-Brown is known for many striking results. These include an approximate solution to Artin's conjecture on primitive roots
, to the effect that out of 3, 5, 7 (or any three similar multiplicatively-independent square-free integer
s), one at least is a primitive root modulo p, for infinitely many prime number
s p.
He also proved that there are infinitely many prime numbers of the form x3 + 2y3.
In collaboration with S. J. Patterson in 1978 he proved the Kummer conjecture on cubic Gauss sums
in its equidistribution form.
He has applied Burgess's method on character sum
s to the ranks of elliptic curves in families.
He proved that every non-singular cubic form over the rational numbers in at least ten variables represents 0.
Heath-Brown also showed that Linnik's constant is less than or equal to 5.5.
The London Mathematical Society
has awarded Heath-Brown the Junior Berwick Prize (1981), the Senior Berwick Prize (1996), and the Pólya Prize
(2009). He was made a Fellow of the Royal Society in 1993, and a corresponding member of the Göttingen Academy of Sciences
in 1999.
On 13 October 2010, in reference to the fact that a mother had given birth to three babies on the same date in different years, Heath Brown was quoted in the Daily Mail as stating that: "...the odds of the couple's children all being born on the same date were 48,627,125 to one." A number of readers appended comments to the article disagreeing with Heath-Brown's calculations.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working in the field of analytic number theory
Analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...
. He was an undergraduate and graduate student of Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
; his research supervisor was Alan Baker. In 1979 he moved to the University of Oxford
University of Oxford
The University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...
, where since 1999 he has held a professorship in pure mathematics
Pure mathematics
Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of...
.
Heath-Brown is known for many striking results. These include an approximate solution to Artin's conjecture on primitive roots
Artin's conjecture on primitive roots
In number theory, Artin's conjecture on primitive roots states that a given integer a which is not a perfect square and not −1 is a primitive root modulo infinitely many primes p. The conjecture also ascribes an asymptotic density to these primes...
, to the effect that out of 3, 5, 7 (or any three similar multiplicatively-independent square-free integer
Square-free integer
In mathematics, a square-free, or quadratfrei, integer is one divisible by no perfect square, except 1. For example, 10 is square-free but 18 is not, as it is divisible by 9 = 32...
s), one at least is a primitive root modulo p, for infinitely many prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s p.
He also proved that there are infinitely many prime numbers of the form x3 + 2y3.
In collaboration with S. J. Patterson in 1978 he proved the Kummer conjecture on cubic Gauss sums
Kummer sum
In mathematics, Kummer sum is the name given to certain cubic Gauss sums for a prime modulus p, with p congruent to 1 modulo 3. They are named after Ernst Kummer, who made a conjecture about the statistical properties of their arguments, as complex numbers...
in its equidistribution form.
He has applied Burgess's method on character sum
Character sum
In mathematics, a character sum is a sum\Sigma \chi\,of values of a Dirichlet character χ modulo N, taken over a given range of values of n. Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an...
s to the ranks of elliptic curves in families.
He proved that every non-singular cubic form over the rational numbers in at least ten variables represents 0.
Heath-Brown also showed that Linnik's constant is less than or equal to 5.5.
The London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
has awarded Heath-Brown the Junior Berwick Prize (1981), the Senior Berwick Prize (1996), and the Pólya Prize
Pólya Prize (LMS)
The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – those in which the De Morgan Medal is not awarded...
(2009). He was made a Fellow of the Royal Society in 1993, and a corresponding member of the Göttingen Academy of Sciences
Göttingen Academy of Sciences
The Göttingen Academy of Sciences is the second oldest of the seven academies of sciences in Germany. It has the task of promoting research under its own auspices and in collaboration with academics in and outside Germany...
in 1999.
On 13 October 2010, in reference to the fact that a mother had given birth to three babies on the same date in different years, Heath Brown was quoted in the Daily Mail as stating that: "...the odds of the couple's children all being born on the same date were 48,627,125 to one." A number of readers appended comments to the article disagreeing with Heath-Brown's calculations.