AOL Atkin

Arthur Oliver Lonsdale Atkin , quoted as AOL Atkin, he himself used the first name Oliver, (born July 31, 1925 in Liverpool , Merseyside , † December 28, 2008 in Maywood (Illinois) ) was a British-American mathematician who himself dealt with number theory and modular functions .

Life

Atkin worked on the deciphering of German codes in Bletchley Park in the so-called Newmanry during World War II (directed by Max Newman and Shaun Wylie ). In 1952 he received his doctorate with John Edensor Littlewood at Cambridge University ( Two problems in additive number theory ). He was a professor at the University of Durham from the 1950s and at the University of Illinois at Chicago from the 1970s . He died of pneumonia while hospitalized as a result of a fall.

Like Noam Elkies, he improved René Schoof's algorithm for determining the number of points on elliptic curves over finite bodies in the early 1990s .

With François Morain in 1993 he improved a prime number test with elliptic curves by Shafi Goldwasser and Joe Kilian (1986).

With Daniel J. Bernstein he introduced a fast prime number sieve in 2004 ( sieve by Atkin ).

He also dealt with the partition function and module functions , where he is known for the Atkin-Lehner theory of modular forms (with Joseph Lehner ). He also dealt with the moonshine properties of modular shapes in relation to the monster group . With Paul Fong and Stephen D. Smith he proved the existence of such a representation of the monster group, which resulted in the moonlight properties, by computer calculations , it was constructed by Igor Frenkel , James Lepowsky and Arne Meurman .

In the 1960s he used the Atlas Laboratory data center in Chilton for calculations in the theory of module functions (as the first Atlas Research Fellow). In some cases he worked together with Peter Swinnerton-Dyer (Atkin-Swinnerton-Dyer congruences, proven by Anthony Scholl ).

literature

• Atkin, Bryan John Birch (eds.): Computers in Number Theory, Oxford 1969 . Conference organized by the Atlas Computer Laboratory, Academic Press 1971. ( Participant photo in web archive)
• Atkin: Intelligent primality test offer . In: DA Buell, JT Teitelbaum (ed.): Computational perspectives on number theory. Proceedings of a Conference in Honor of AOL Atkin . In: AMS / IP Studies in Advanced Mathematics , Vol. 7, 1998, pp. 1–12

Individual evidence

1. ↑ Atkin-Goldwasser-Kilian-Morain certificate or algorithm for proof of primality, article on it. Math World. Atkin, Morain: Elliptic curves and primality proving . In: Mathematics of Computation , Volume 61, 1993, pp. 29-68
2. ^ Atkin, Bernstein: Prime sieves using binary quadratic forms . In: Mathematics of Computation , Volume 73, 2004, pp. 1023-1030
3. ↑ Atkin, J. Lehner: Hecke operators on ${\displaystyle \Gamma _{0}(m)}$ . In: Mathematische Annalen , Volume 185, 1970, pp. 134-160, uni-goettingen.de
4. ^ Originally found by John McKay , John Horton Conway and Simon Norton and explained by representations in a vertex operator algebra by Frenkel, Lepowsky, Meurman and proven by Richard Borcherds .
5. ↑ founded in 1964, assigned to the Rutherford Laboratory
6. ^ Bryan Birch : Atkin at the Atlas Lab . In: Buell, Teitelbaum (Ed.): Computational perspectives in number theory . 1998. As Birch wrote, the theory of modular functions was completely out of fashion at the time (in England Robert Alexander Rankin was still active in it at the time ). However, his calculations were used to show errors in the machine's hardware.