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Professor Christopher Hooley FRS

15 January 2019

It is with great sadness that we learned of the death of Professor Christopher Hooley.

Professor Christopher Hooley was one of the UK’s most distinguished Number Theorists and Head of the Cardiff School of Mathematics.

Professor Hooley graduated from Corpus Christi College, Cambridge and went on to complete his PhD there in 1957 entitled ‘Some Theorems in the Additive Theory of Numbers’ under the supervision of Professor A. Ingham.

In 1958 Professor Hooley moved to Bristol, and stayed there until 1965 when he was appointed Professor of Pure Mathematics at Durham. In 1967 he moved to Cardiff as Head of the Pure Mathematics School and was the Head of Cardiff School of Mathematics from 1988-1995. Professor Hooley was a Distinguished Research Professor at Cardiff until 2008.

In 1973 he won the Adams Prize awarded by Cambridge University, and in 1980 the Senior Berwick Prize from the London Mathematical Society. In 1983, Professor Hooley delivered a one hour address at the International Congress of Mathematicians in Warsaw. He was on several occasions a visiting Professor at the Institute for Advanced Study at Princeton, and in 1983 was elected a fellow of the Royal Society. Professor Hooley was a Founding Fellow of the Learned Society of Wales.

Professor Hooley had nearly a hundred publications that have strongly influenced the development of analytic number theory through the past half century. He made pivotal contributions to the development of sieve theory, some of this work having been exposed in his influential monograph “Applications of Sieve Methods”, published by Cambridge University Press in 1976.

He was an early pioneer in analytic number theory of the application of Deligne’s celebrated resolution of the Weil Conjectures to problems in sieve theory and Diophantine equations. This work shifted the course of the subject.

Professor Hooley’s work on additive problems and in applications of the circle method is unique in its flavour and unparalleled in its sophistication. In particular, his proof in 1988 that non-singular cubic forms in nine variables satisfy the Hasse Principle remains one of the crowning achievements of the use of Fourier analytic methods within number theory.

Finally, but by no means least, there is his encyclopaedic series of nineteen papers on the Barban-Davenport-Halberstam theorem.

Significant papers include:

  • On nonary cubic forms, Journal für die reine und angewandte Mathematik, 386 , pages 32-98, (1988)
  • On the Barban-Davenport-Halberstam theorem V, VI, and VII, Proc.London Math. Soc. (3), 33 (1976), 535-548; J. London Math. Soc. (2), 13 (1976), 57-64; ibid 16 (1977), 1-8
  • On the representation of a number as a sum of four cubes I, and II, Proc. London Math. Soc. (3), 36 (1978), 117-140; J. London Math Soc. (2), 16 (1977), 424-428.
  • On a new technique and its applications to the theory of numbers, Proc. London Math. Soc. (3), 38 (1979), 115-151.

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