| Citation | Distinguished first for his contributions to the additive theory of numbers and in particular, for his demonstration of the asymptotic formula for the eight cubes problem, the proof of which had eluded many eminent predecessors. Secondly, for his discovery of an important identity - now known as Vaughan's identity -, which has been very influential in recent number theory and which played a substantial role in the recent elucidation of the Kummer conjecture by Heath-Brown and Patterson. Also, for his fundamental work in multiplicative number theory done either alone or in collaboration with Montgomery, including a recent proof of a long-standing conjecture due to Erdos concerning the distribution of numbers relatively prime to a given large number n. He was awarded the Junior Berwick Prize of the London Mathematical Society, 1979. |