29 October 1925 |
Breslau, Province of Lower Silesia, Germany
|Doctoral advisor||Theodor Estermann|
|Known for||diophantine approximation
|Notable awards||Sylvester Medal (1991)
LMS De Morgan Medal (1983)
Fellow of the Royal Society (1960)
Fields Medal (1958)
Klaus Friedrich Roth (born 29 October 1925) is a German-born British mathematician known for work on diophantine approximation, the large sieve, and irregularities of distribution. He was born in Breslau, Prussia, but was raised and educated in the UK. He was pupil at St. Paul's School in London from 1939 to 1943 and then attended Cambridge University, graduating from Peterhouse, Cambridge in 1945. In 1946 he began research at University College London, under the supervision of Theodor Estermann.
In 1952, Roth proved that subsets of the integers of positive density must contain infinitely many arithmetic progressions of length three, thus establishing the first non-trivial case of what is now known as Szemerédi's theorem. His definitive result, now known usually as the Thue–Siegel–Roth theorem, but also just Roth's theorem, dates from 1955, when he was a lecturer at University College London. He was awarded a Fields Medal in 1958 on the strength of it. He became a professor at University College London in 1961, and moved to a chair at Imperial College London in 1966, a position he retained until official retirement at 1988. He then changed his status to visiting professor and remained at Imperial College until 1996.
- Roth, Klaus Friedrich (1955), "Rational approximations to algebraic numbers", Mathematika 2: 1–20, 168, doi:10.1112/S0025579300000644, ISSN 0025-5793, MR 0072182
- Halberstam, Heini; Roth, Klaus Friedrich (1983) , Sequences (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-90801-4, MR 0210679
- Davenport, H. (1960), "The work of K. F. Roth", Proc. Internat. Congress Math. 1958, Cambridge University Press, pp. lvii–lx, Zbl 0119.24901
- Chen, W. W. L.; Gowers, W. T.; Halberstam, H. et al., eds. (2009), "Klaus Roth at 80", Analytic number theory. Essays in honour of Klaus Roth on the occasion of his 80th birthday, Cambridge: Cambridge University Press, ISBN 978-0-521-51538-2, Zbl 1155.11004
- O'Connor, John J.; Robertson, Edmund F., "Klaus Roth", MacTutor History of Mathematics archive, University of St Andrews.
- Klaus Roth at the Mathematics Genealogy Project