Harold Davenport

Harold Davenport
Harold Davenport in 1968
Born	(1907-10-30)30 October 1907 Huncoat, Accrington, Lancashire, England
Died	9 June 1969(1969-06-09) (aged 61) Cambridge, England
Residence	United Kingdom
Nationality	English
Fields	Mathematician
Institutions	University of Wales University College London University of Cambridge
Alma mater	University of Manchester Trinity College, Cambridge
Doctoral advisor	John Edensor Littlewood
Doctoral students	John Horton Conway Alan Baker Peter Elliott H. L. Montgomery Martin Huxley
Known for	Number theory Davenport–Schinzel sequence
Notable awards	Rayleigh Prize (1930) Adams Prize (1940) Senior Berwick Prize (1954) Sylvester Medal (1967) Fellow of the Royal Society
Children	James H. Davenport

Harold Davenport FRS (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory.

Born in Huncoat, Accrington, Lancashire, he was educated at Accrington Grammar School, the University of Manchester, where he graduated in 1927, and Trinity College, Cambridge. He became a research student of John Edensor Littlewood, working on the question of the distribution of quadratic residues.

The attack on the distribution question leads quickly to problems that are now seen to be special cases of those on local zeta-functions, for the particular case of some special hyperelliptic curves such as ${\displaystyle Y^{2}=X(X-1)(X-2)\ldots (X-k)}$.

Bounds for the zeroes of the local zeta-function immediately imply bounds for sums ${\displaystyle \sum \chi (X(X-1)(X-2)\ldots (X-k))}$, where χ is the Legendre symbol modulo a prime number p, and the sum is taken over a complete set of residues mod p.