Andrew Ogg

Andrew Pollard Ogg ( born April 9, 1934 in Bowling Green ( Ohio)) is an American mathematician who deals with number theory and modular forms.

Life

Ogg in 1961 received his doctorate from Harvard University with John T. Tate ( " Cohomology of abelian varieties over function fields" ). He was a professor at the University of California, Berkeley.

Ogg has been dealing with the arithmetic theory of elliptic curves ( ie, the rational points ). His suspicions about the possible Torsionsuntergruppen of the groups of rational points on elliptic curves were proven in 1977 by Barry Mazur ( Ogg achieved partial results, by examining modular elliptic curves). Ogg was also the first who suspected a connection between the monster group and modular functions in the 1970s - a study area, which is known as " monstrous moonshine " (including John Horton Conway, Richard Borcherds ). On the one hand, there are few primes p for which yields the compactification of H \ with the Kongruenzuntergruppen of which act as Möbius transformations in the upper complex half- plane H, a Riemann surface of genus 0. The body of the module functions, on these surfaces is then generated by a single function, the "main module". These primes are after an observation of Ogg but exactly 15 prime numbers ( p = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71), the order of the Share the Monster group.

Writings

• Introduction to modular forms and Dirichlet Series. Benjamin 1969