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David Rodney "Roger" Heath-Brown F.R.S. (born 12 October 1952),〔(【引用サイトリンク】url=http://www.debretts.com/people/biographies/browse/h/18035/David%20Rodney%20%28Roger%29+HEATH-BROWN.aspx )〕 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) 〕 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.〔D.R. Heath-Brown, ''The density of rational points on curves and surfaces'', Annals of Mathematics, 155(2), pages 553-598 (2002)〕 This particular conjecture of Serre was later dubbed the ``dimension growth conjecture" and this was almost completely solved by various works of Browning, Heath-Brown, and Salberger by 2009 〔T. D. Browning, ''Quantitative Arithmetic of Projective Varieties'', Progress in Mathematics, 277, Birkhauser〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Roger Heath-Brown」の詳細全文を読む スポンサード リンク
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