Roger Heath-Brown
David Rodney "Roger" Heath-Brown (born 12 October 1952) is a British mathematician working in the field of analytic number theory. Education He was an undergraduate and graduate student of Trinity College, Cambridge; his research supervisor was Alan Baker. Career and research In 1979 he moved to the University of Oxford, where from 1999 he held a professorship in pure mathematics. He retired in 2016. Heath-Brown is known for many striking results. He 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 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. Heath-Brown also showed that Linnik's constant is less than or equal to 5.5. More recently, Heath-Brown is known for his pioneering work on the so-called determinant method. Using this method he was able to prove a conjecture of Serre in the four variable case in 2002. This particular conjecture of Serre was later dubbed the "dimension growth conjecture" and