Harold Davenport: Difference between revisions
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==Books== |
==Books== |
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*''The Higher Arithmetic: An Introduction to the Theory of Numbers'' (1952)<ref>{{cite journal|author=Bateman, P. T.|authorlink=Paul T. Bateman|title=Review: ''The higher arithmentic'', by H. Davenport|journal=Bull. Amer. Math. Soc.|year=1953|volume=59|issue=5|pages=473–474|url=http://www.ams.org/journals/bull/1953-59-05/S0002-9904-1953-09724-5/S0002-9904-1953-09724-5.pdf}}</ref> |
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*''The Higher Arithmetic: An Introduction to the Theory of Numbers'' (1952) |
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*''Analytic methods for Diophantine equations and Diophantine inequalities'' (1962) |
*''Analytic methods for Diophantine equations and Diophantine inequalities'' (1962) |
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*''Multiplicative number theory ''(1967)<ref>{{cite journal|author=Stark, H. M.|authorlink=Harold Stark|title=Review: ''Introduction to analytic number theory'', by K. Chandrasekharan; ''Arithmetic functions'', by K. Chandrasekharan; ''Multiplicative number theory'', by Harold Davenport; ''Sequences'', by H. Halberstam and K. F. Roth''|journal=Bull. Amer. Math. Soc.|year=1971|volume=77|issue=6|pages=943–957|url=http://www.ams.org/journals/bull/1971-77-06/S0002-9904-1971-12812-4/S0002-9904-1971-12812-4.pdf}}</ref> |
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*''Multiplicative number theory ''(1967) |
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*'' The collected works of Harold Davenport'' (1977) in four volumes, edited by [[B. J. Birch]], [[H. Halberstam]], [[C. A. Rogers]]<ref>{{cite journal|author=Grosswald, Emil|authorlink=Emil Grosswald|title=Review: B. J. Birch, H. Halberstam, and C. A. Rogers, ''The collected works of Harold Davenport''|journal=Bull. Amer. Math. Soc. (N.S.)|year=1979|volume=1|issue=4|pages=668–675|url=http://projecteuclid.org/euclid.bams/1183544581}}</ref> |
*'' The collected works of Harold Davenport'' (1977) in four volumes, edited by [[B. J. Birch]], [[H. Halberstam]], [[C. A. Rogers]]<ref>{{cite journal|author=Grosswald, Emil|authorlink=Emil Grosswald|title=Review: B. J. Birch, H. Halberstam, and C. A. Rogers, ''The collected works of Harold Davenport''|journal=Bull. Amer. Math. Soc. (N.S.)|year=1979|volume=1|issue=4|pages=668–675|url=http://projecteuclid.org/euclid.bams/1183544581}}</ref> |
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Revision as of 14:00, 2 April 2014
Harold Davenport | |
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Born | Huncoat, Accrington, Lancashire, England | 30 October 1907
Died | 9 June 1969 Cambridge, England | (aged 61)
Nationality | English |
Alma mater | University of Manchester Trinity College, Cambridge |
Known for | Number theory Davenport–Schinzel sequence |
Children | James H. Davenport |
Awards | Fellow of the Royal Society[1] |
Scientific career | |
Fields | Mathematician |
Institutions | University of Wales University College London University of Cambridge |
Doctoral advisor | John Edensor Littlewood[2] |
Doctoral students | John Horton Conway Alan Baker Peter Elliott H. L. Montgomery Martin Huxley[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 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,[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 Legendre symbol modulo a prime number p, and the sum is taken over a 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 University of Manchester in 1937, just at the time when Louis Mordell had recruited émigrés from continental Europe to build an outstanding department. He moved into the areas of diophantine approximation and geometry of numbers. These were fashionable, and complemented the technical expertise he had in 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 London Mathematical Society from 1957 to 1959.[3] After professorial positions at the University of Wales and University College London, he was appointed to 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 University College of North Wales at Bangor, in 1944; they had two children, Richard and James.[4] James is Hebron and Medlock Professor of Information Technology at the University of Bath.
Influence
From about 1950 he was the obvious leader of a "school", somewhat unusually in the context of British mathematics. The successor to the school of mathematical analysis of G. H. Hardy and 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)
- Multiplicative number theory (1967)[6]
- The collected works of Harold Davenport (1977) in four volumes, edited by B. J. Birch, H. Halberstam, C. A. Rogers[7]
References
- ^ a b Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1098/rsbm.1971.0006, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1098/rsbm.1971.0006
instead. - ^ a b c Harold Davenport at the Mathematics Genealogy Project
- ^ P.R. Cooper. "Presidents of the London Mathematical Society". Retrieved 22 February 2007.
- ^ O'Connor, John J.; Robertson, Edmund F., "Harold Davenport", MacTutor History of Mathematics Archive, University of St Andrews
- ^ Bateman, P. T. (1953). "Review: The higher arithmentic, by H. Davenport" (PDF). Bull. Amer. Math. Soc. 59 (5): 473–474.
- ^ Stark, H. M. (1971). "Review: Introduction to analytic number theory, by K. Chandrasekharan; Arithmetic functions, by K. Chandrasekharan; Multiplicative number theory, by Harold Davenport; Sequences, by H. Halberstam and K. F. Roth" (PDF). Bull. Amer. Math. Soc. 77 (6): 943–957.
- ^ Grosswald, Emil (1979). "Review: B. J. Birch, H. Halberstam, and C. A. Rogers, The collected works of Harold Davenport". Bull. Amer. Math. Soc. (N.S.). 1 (4): 668–675.
- Use dmy dates from August 2011
- British mathematicians
- Number theorists
- Fellows of the Royal Society
- Academics of the University of Wales
- Academics of University College London
- Academics of the Victoria University of Manchester
- Alumni of the Victoria University of Manchester
- Alumni of Trinity College, Cambridge
- Fellows of Trinity College, Cambridge
- 1907 births
- 1969 deaths
- Cancer deaths in England
- Deaths from lung cancer
- People educated at Accrington Grammar School
- People from Accrington