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Roger Heath-Brown
From Wikipedia, the free encyclopedia
David Rodney ("Roger") Heath-Brown, F.R.S., 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. He is Professor at the Mathematical Institute of the University of Oxford.
He is known for many striking results. These include an approximate solution to the Artin 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.
In collaboration with S. J. Patterson, he in 1978 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.[1]
Heath-Brown also showed that Linnik's constant is less than or equal to 5.5.[2]
- ^ D. R. Heath-Brown, Cubic forms in ten variables, Proceedings of the London Mathematical Society, 47(3), pages 225-257 (1983)
- ^ 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)