Andrew Ogg

Andrew Ogg (1999)

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

Ogg was particularly concerned with the arithmetic theory of elliptic curves (that is, their rational points ). His conjectures about the possible torsional subsets of the groups of rational points on elliptic curves were proven in 1977 by Barry Mazur (Ogg obtained partial results by studying modular elliptic curves). Ogg was also the first in the 1970s to suspect a connection between the monster group and module functions - an area of ​​study known as "monstrous moonshine" (including John Horton Conway , Richard Borcherds ). On the one hand, there are few prime numbers p for which the compactification of H \ with the congruence subgroups of , which act as Möbius transformations in the upper complex half-plane H, results in a Riemann surface of gender 0. The body of the module functions on these surfaces is then generated by a single function, the “main module”. According to an observation by Ogg, these prime numbers are exactly the 15 prime numbers (p = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71) that make up the order of the monster group. ${\displaystyle \Gamma _{0}(p)}$ ${\displaystyle \Gamma _{0}(p)}$ ${\displaystyle SL(2,\mathbb {R} )}$

Fonts

• Introduction to modular forms and Dirichlet Series . Benjamin 1969

Web links

• Page at the University of Berkeley
• Ogg "Rational points of finite order on elliptic curves", Inventiones Mathematicae, Vol. 12, 1971, p. 105