| Harold Davenport | |
 Harold Davenport in 1968
|
|
| Born | 30 October 1907 Huncoat, Lancashire, England |
|---|---|
| Died | 9 June 1969 (aged 61) Cambridge, England |
| Residence |  UK |
| Nationality | English |
| Fields | Mathematician |
| Institutions | University of Wales University College London University of Cambridge |
| Alma mater | Victoria University of Manchester University of Cambridge |
| Doctoral advisor | J. E. Littlewood |
| Doctoral students | John Horton Conway Alan Baker H. L. Montgomery |
| Known for | Number theory |
Harold Davenport (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory. Events 637 - Antioch surrenders to the Muslim forces under Rashidun Caliphate after the Battle of Iron bridge. Year 1907 ( MCMVII) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Common year Huncoat is a small village in Lancashire, England; situated in the North West. Lancashire is a non-metropolitan county of historic origin in the North West of England, bounded to the west by the Irish Sea England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland Events 53 - Roman Emperor Nero marries Claudia Octavia 62 - Claudia Octavia commits Year 1969 ( MCMLXIX) was a Common year starting on Wednesday (link will display full calendar of the Gregorian calendar. The city of Cambridge (ˈkeɪmbrɪdʒ is a university town and the administrative centre of the county of Cambridgeshire, England England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland A mathematician is a person whose primary area of study and research is the field of Mathematics. The University of Wales ( Prifysgol Cymru in Welsh) is a confederal University founded in 1893. University College London ( UCL) is a multi-faculty university institution based in the United Kingdom and a constituent college of the University of London The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval The Victoria University of Manchester (commonly known as the University of Manchester) was a University in Manchester, England. The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the A doctorate is an Academic degree that indicates the highest level of academic achievement John Edensor Littlewood ( 9 June 1885 &ndash 6 September 1977) was a British Mathematician, best known for his long collaboration John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups Alan Baker (born on August 19 1939) is an English Mathematician. Hugh Montgomery can be Hugh Montgomery 1st Viscount of the Great Ardes Hugh Montgomery (mathematician, an American mathematician Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes Events 637 - Antioch surrenders to the Muslim forces under Rashidun Caliphate after the Battle of Iron bridge. Year 1907 ( MCMVII) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Common year Events 53 - Roman Emperor Nero marries Claudia Octavia 62 - Claudia Octavia commits Year 1969 ( MCMLXIX) was a Common year starting on Wednesday (link will display full calendar of the Gregorian calendar. Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes
Contents |
Early life
Born in Huncoat, Lancashire, he was educated at Accrington Grammar School, the University of Manchester, where he graduated in 1927, and Trinity College, Cambridge. Huncoat is a small village in Lancashire, England; situated in the North West. Lancashire is a non-metropolitan county of historic origin in the North West of England, bounded to the west by the Irish Sea Accrington is a town within the Hyndburn borough of Lancashire, in North West England. The University of Manchester is a " red brick " civic University located in Manchester, England. Year 1927 ( MCMXXVII) was a Common year starting on Saturday (link will display full calendar of the Gregorian calendar. Trinity College is a constituent college of the University of Cambridge in Cambridge, England. He became a research student of J. E. Littlewood, working on the question of the distribution of quadratic residues. John Edensor Littlewood ( 9 June 1885 &ndash 6 September 1977) was a British Mathematician, best known for his long collaboration An Integer q is called a quadratic residue modulo n if it is congruent to a perfect square (mod n) i
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
- Y2 = X(X − 1) (X − 2) . In Number theory, a local zeta-function is a Generating function Z ( t) for the number of solutions of a set of equations In Algebraic geometry, a hyperelliptic curve (over the Complex numbers) is an Algebraic curve given by an equation of the form y^2 = f(x . . (X − k).
Bounds for the zeroes of the local zeta-function immediately imply bounds for sums
- Σ χ(x(x − 1) (x − 2) . . . (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. The Legendre symbol or quadratic character is a function introduced by Adrien-Marie Legendre in 1798 during his partly successful attempt to prove the Law of In Mathematics, modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of Arithmetic for Integers In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 In Mathematics, modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of Arithmetic for Integers
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. Year 1932 ( MCMXXXII) was a Leap year starting on Friday of the Gregorian calendar. Year 1933 ( MCMXXXIII) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar. Marburg is a city in Hesse, Germany, on the River Lahn. It is the main town of the Marburg-Biedenkopf district Göttingen ( ˈgœtɪŋən, Low German: Chöttingen is a College town in Lower Saxony, Germany. Helmut Hasse (ˈhasə ( 25 August 1898 – 26 December 1979) was a German Mathematician working in Algebraic This produced the work on the Hasse-Davenport relations for Gauss sums, and contact with Hans Heilbronn, with whom Davenport would later collaborate. The Hasse–Davenport relation, named after Helmut Hasse and Harold Davenport, is an equality in Number theory relating Gauss sums One of its In Mathematics, a Gauss sum or Gaussian sum is a particular kind of finite sum of Roots of unity, typically G (&chi &psi = Hans Arnold Heilbronn ( 8 October 1908, Berlin – 28 April 1975, Toronto) was a mathematician 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. Algebraic geometry is a branch of Mathematics which as the name suggests combines techniques of Abstract algebra, especially Commutative algebra, with Emil Artin ( March 3, 1898, in Vienna – December 20, 1962, in Hamburg) was an Austrian Mathematician Amalie Emmy Noether, ˈnøːtɐ (23 March 1882 – 14 April 1935 was a German Mathematician known for her groundbreaking contributions to Abstract algebra and Abstract algebra is the subject area of Mathematics that studies Algebraic structures such as groups, rings, fields, modules
Later career
He took an appointment at the University of Manchester in 1937, just at the time when Louis Mordell had recruited emigrés from continental Europe to build an outstanding department. The School of Mathematics at the University of Manchester is one of the largest mathematics departments in the United Kingdom, with around 80 academic staff and an Year 1937 ( MCMXXXVII) was a Common year starting on Friday (link will display the full calendar of the Gregorian calendar. Louis Joel Mordell ( 28 January 1888 - 12 March 1972) was a British mathematician known for pioneering research in Number theory. He moved into the areas of diophantine approximation and geometry of numbers. In Number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of Real numbers by Rational In Number theory, the geometry of numbers is a topic and method arising from the work of Hermann Minkowski, on the relationship between Convex sets and 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. In Mathematics, the Hardy–Littlewood circle method is one of the most frequently used techniques of Analytic number theory. The Riemann hypothesis (also called the Riemann zeta-hypothesis) first formulated by Bernhard Riemann in 1859 is one of the most famous and important unsolved
He was President of the London Mathematical Society from 1957 to 1959. The London Mathematical Society ( LMS) is the leading mathematical society in England. Year 1957 ( MCMLVII) was a Common year starting on Tuesday (link displays the 1957 Gregorian calendar) The year 1959 ( MCMLIX) was a Common year starting on Thursday (link will display full calendar of the Gregorian calendar. [1] 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. The University of Wales ( Prifysgol Cymru in Welsh) is a confederal University founded in 1893. University College London ( UCL) is a multi-faculty university institution based in the United Kingdom and a constituent college of the University of London See also Rouse Ball Professor of English Law The Rouse Ball Professorship of Mathematics is one of the senior chairs in the Mathematics Departments at Year 1958 ( MCMLVIII) was a Common year starting on Wednesday (link will display full calendar of the Gregorian calendar. There he remained until his death, of lung cancer. Lung cancer is a Disease of uncontrolled Cell growth in tissues of the Lung.
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. James Harold Davenport (born 1953 is a British Computer scientist who works in Computer algebra. [2] James is Hebron and Medlock Professor of Information Technology at the University of Bath. The University of Bath is a Campus university located in Bath, England.
Influence
From about 1950 he was the obvious leader of a "school", somewhat unusually in the context of British mathematics. Year 1950 ( MCML) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar. 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. Analysis has its beginnings in the rigorous formulation of Calculus. Godfrey Harold Hardy FRS ( February 7, 1877 Cranleigh, Surrey, England &ndash December 1, 1947 John Edensor Littlewood ( 9 June 1885 &ndash 6 September 1977) was a British Mathematician, best known for his long collaboration The 1930s were described as an abrupt shift to more radical and conservative lifestyles as countries were struggling to find a solution to the Great Depression. 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. Klaus Friedrich Roth, (ˈroʊθ (b 29 October 1925) is a British Mathematician known for work on Diophantine approximation, the Large Alan Baker (born on August 19 1939) is an English Mathematician. 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. Combinatorics is a branch of Pure mathematics concerning the study of discrete (and usually finite) objects This concrete emphasis on problems stood in sharp contrast with the abstraction of Bourbaki, who were then active just across the English Channel. Nicolas Bourbaki is the collective Pseudonym under which a group of (mainly French) 20th-century Mathematicians wrote a series of books presenting an exposition
Books
- The Higher Arithmetic (1952)
- Analytic methods for Diophantine equations and Diophantine inequalities (1962)
- Multiplicative number theory (1967)
- The collected works of Harold Davenport (1977) in four volumes, edited by B. J. Birch, H. Halberstam, C. Bryan John Birch FRS (born 1931 is a British mathematician His name has been given to the Birch and Swinnerton-Dyer conjecture. Heini Halberstam is a British Mathematician, working in the field of Analytic number theory. A. Rogers
Notes
- ^ P. R. Cooper. Presidents of the London Mathematical Society. Retrieved on 2007-02-22. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1495 - King Charles VIII of France enters Naples to claim the city's throne
- ^ O'Connor, John J. ; Robertson, Edmund F. . Harold Davenport. MacTutor History of Mathematics archive. University of St Andrews. Retrieved on 2008-01-19. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 1419 - Hundred Years' War: Rouen surrenders to Henry V of England completing his reconquest of Normandy.
References
- C. A. Rogers, B. J. Birch, H. Halberstam, D. A. Burgess, "Harold Davenport. 1907–1969", Biographical Memoirs of Fellows of the Royal Society, Vol. 17, 1971, pp. 159–192.
External links
- O'Connor, John J. & Robertson, Edmund F. , “Harold Davenport”, MacTutor History of Mathematics archive
- Harold Davenport at the Mathematics Genealogy Project
| Persondata | |
|---|---|
| NAME | Davenport, Harold |
| ALTERNATIVE NAMES | |
| SHORT DESCRIPTION | English Mathematician |
| DATE OF BIRTH | 30 October 1907 |
| PLACE OF BIRTH | Huncoat, Lancashire, England |
| DATE OF DEATH | 9 June 1969 |
| PLACE OF DEATH | Cambridge, England |
Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic