Roger Heath-Brown

Roger Heath-Brown
Born	12 October 1952 (1952-10-12) (age 59)
Residence	United Kingdom
Citizenship	United Kingdom
Fields	Pure mathematician
Institutions	University of Oxford
Alma mater	University of Cambridge
Doctoral advisor	Alan Baker
Known for	Analytic number theory
Notable awards	Pólya Prize (2009) Fellow of the Royal Society (1993)

David Rodney "Roger" Heath-Brown F.R.S. (born 12 October 1952),^[1] 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.^[1]

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 integers), one at least is a primitive root modulo p, for infinitely many prime numbers p. He also proved that there are infinitely many prime numbers of the form x³ + 2y³.^[2] 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 sums 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.^[3] Heath-Brown also showed that Linnik's constant is less than or equal to 5.5.^[4]

The London Mathematical Society has awarded Heath-Brown the Junior Berwick Prize (1981), the Senior Berwick Prize (1996),^[5] and the Pólya Prize (2009). He was made a Fellow of the Royal Society in 1993,^[1] and a corresponding member of the Göttingen Academy of Sciences in 1999.^[6]

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. ^[7]

See also

• Heath-Brown–Moroz constant

References

1. ^ ^{a b c} "Prof Roger Heath-Brown, FRS". Debrett's People of Today. http://www.debretts.com/people/biographies/browse/h/18035/David%20Rodney%20%28Roger%29+HEATH-BROWN.aspx. Retrieved 28 December 2010. 
2. ^ Heath-Brown, D.R. (2001). "Primes represented by x³ + 2y³". Acta Mathematica 186: 1–84. doi:10.1007/BF02392715.  edit
3. ^ D. R. Heath-Brown, Cubic forms in ten variables, Proceedings of the London Mathematical Society, 47(3), pages 225–257 (1983) doi:10.1112/plms/s3-47.2.225
4. ^ D. R. Heath-Brown, Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression, Proceedings of the London Mathematical Society, 64(3), pages 265–338 (1992) doi:10.1112/plms/s3-64.2.265
5. ^ Berwick prizes page at The MacTutor History of Mathematics archive
6. ^ "Professor Roger Heath-Brown". The Mathematical Institute, University of Oxford. http://www.maths.ox.ac.uk/contact/details/rhb. Retrieved 28 December 2010. 
7. ^ Levy, Andrew (13 October 2010). "Daily Mail article". London. http://www.dailymail.co.uk/news/article-1320113/Happy-birthday-Couple-3-children-born-date.html. 

External links

• Official home page
• Roger Heath-Brown at the Mathematics Genealogy Project.

Persondata
Name	Heath-Brown, Roger
Alternative names
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Date of birth	12 October 1952
Place of birth
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