Bryan Birch

Bryan John Birch (born September 25, 1931 in Burton-upon-Trent ) is a British mathematician who deals with number theory. He is a professor at Oxford University .

Birch received his doctorate in 1958 from John Cassels in Cambridge ( The geometry of numbers ). At that time he mainly worked as a student of Harold Davenport , where he obtained important results with the Hardy-Littlewood circle method of analytical number theory (Birch's theorem, forms of odd degrees in rational numbers have zeros for a sufficiently large number of variables). He is best known for the conjecture made by Birch and Swinnerton-Dyer in the 1960s with Peter Swinnerton-Dyer about the arithmetic information that results from the behavior of the zeta function of elliptical curves at one of their zeros. Birch and Swinnerton-Dyer supported their conjecture with extensive computer calculations. The conjecture is still open today and is an important motor in the development of arithmetic algebraic geometry. Birch also worked on Heegner points of elliptic curves and algebraic K-theory (Birch- Tate conjecture). For the explicit calculation with modular forms in the context of computer algebra, he introduced important module symbols, especially developed by John Cremona , who did his doctorate on this subject with him in 1981.

Birch has been a Fellow of the Royal Society since 1972 . In 1993 he received the Senior Whitehead Prize and in 2007 the De Morgan Medal of the London Mathematical Society . For 2020 Birch was awarded the New Year's Eve Medal of the Royal Society.In 1966 he was invited speaker at the International Congress of Mathematicians in Moscow (Rational Points on Elliptic Curves). He is a fellow of the American Mathematical Society .

In 1977 he published the collected works of Harold Davenport.

Web links

Individual evidence

^ John E. Cremona: Algorithms for modular elliptic curves. 2nd Edition. Cambridge University Press, Cambridge et al. 1997, ISBN 0-521-59820-6 .

personal data
SURNAME	Birch, Bryan
ALTERNATIVE NAMES	Birch, Bryan John
BRIEF DESCRIPTION	British mathematician
DATE OF BIRTH	September 25, 1931
PLACE OF BIRTH	Burton-upon-Trent

[1] John E. Cremona: Algorithms for modular elliptic curves. 2nd Edition. Cambridge University Press, Cambridge et al. 1997, ISBN 0-521-59820-6 .