# Roger Heath-Brown : biography

**David Rodney "Roger" Heath-Brown** F.R.S. (born 12 October 1952), is a British mathematician working in the field of analytic number theory.

## Life

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 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 *x*3 + 2*y*3. 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.D. R. Heath-Brown, *Cubic forms in ten variables*, Proceedings of the London Mathematical Society, **47**(3), pages 225–257 (1983) Heath-Brown also showed that Linnik’s constant is less than or equal to 5.5.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)

## Awards and honours

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. In 2012 he became a fellow of the American Mathematical Society., retrieved 2013-01-19.