Harold Davenport

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Harold Davenport
Davenport in 1968
Born(1907-10-30)30 October 1907
Huncoat, Lancashire, England
Died9 June 1969(1969-06-09) (aged 61)
Cambridge, England
Alma materUniversity of Manchester
Trinity College, Cambridge
Known for
Children
H. L. Montgomery
Martin Huxley
G. L. Watson[2]

Harold Davenport FRS[1] (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory.

Early life

Born on 30 October 1907 in

Accrington Grammar School, the University of Manchester (graduating in 1927), and Trinity College, Cambridge. He became a research student of John Edensor Littlewood,[2] working on the question of the distribution of quadratic residues
.

First steps in research

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 .

Bounds for the zeroes of the local zeta-function immediately imply bounds for sums , where χ is the

complete set of residues
mod p.

In the light of this connection it was appropriate that, with a Trinity research fellowship, Davenport in 1932–1933 spent time in Marburg and Göttingen working with Helmut Hasse, an expert on the algebraic theory. This produced the work on the Hasse–Davenport relations for Gauss sums, and contact with Hans Heilbronn, with whom Davenport would later collaborate. In fact, as Davenport later admitted, his inherent prejudices against algebraic methods ("what can you do with algebra?") probably limited the amount he learned, in particular in the "new" algebraic geometry and Artin/Noether approach to abstract algebra.

Later career

He took an appointment at the

Hardy–Littlewood circle method; he was later, though, to let drop the comment that he wished he'd spent more time on the Riemann hypothesis
.

He was President of the

Rouse Ball Chair of Mathematics
in Cambridge in 1958. There he remained until his death, of lung cancer.

Personal life

Davenport married Anne Lofthouse, whom he met at the

James, the latter going on to become Hebron and Medlock Professor of Information Technology at the University of Bath.[4]

Influence

From about 1950, Davenport was the obvious leader of a "school", somewhat unusually in the context of British mathematics. The successor to the school of

J. E. Littlewood, it was also more narrowly devoted to number theory, and indeed to its analytic side, as had flourished in the 1930s. This implied problem-solving, and hard-analysis methods. The outstanding works of Klaus Roth and Alan Baker exemplify what this can do, in diophantine approximation. Two reported sayings, "the problems are there", and "I don't care how you get hold of the gadget, I just want to know how big or small it is", sum up the attitude, and could be transplanted today into any discussion of combinatorics. This concrete emphasis on problems stood in sharp contrast with the abstraction of Bourbaki, who were then active just across the English Channel
.

Books

  • The Higher Arithmetic: An Introduction to the Theory of Numbers (1952)[5]
  • Analytic methods for Diophantine equations and Diophantine inequalities (1962); Browning, T. D., ed. (2005). 2nd edition. Cambridge University Press.
    ISBN 0-521-60583-0.[6]
  • Multiplicative number theory (1967)[7]
  • The collected works of Harold Davenport (1977) in four volumes, edited by
    C. A. Rogers[8]

References

Wikimedia Commons has media related to Harold Davenport (mathematician).
  1. ^
    S2CID 123347742
    .
  2. ^ a b c Harold Davenport at the Mathematics Genealogy Project
  3. ^ P.R. Cooper. "Presidents of the London Mathematical Society". Archived from the original on 6 October 2007. Retrieved 22 February 2007.
  4. ^ O'Connor, John J.; Robertson, Edmund F., "Harold Davenport", MacTutor History of Mathematics Archive, University of St Andrews
  5. doi:10.1090/S0002-9904-1953-09724-5
    .
  6. ^ Lozano-Robledo, Álvaro (15 January 2006). "Review of Analytic methods for Diophantine equations and Diophantine inequalities by Harold Davenport". MAA Reviews, Mathematical Association of America.
  7. doi:10.1090/S0002-9904-1971-12812-4
    .
  8. doi:10.1090/s0273-0979-1979-14657-3
    .
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