Ogg worked in algebra and number theory. His accomplishments include the Grothendieck–Ogg–Shafarevich formula, the Néron–Ogg–Shafarevich criterion and the 1975 characterization of supersingular primes, the starting point for the theory of monstrous moonshine. He is also the author of the book Modular forms and Dirichlet series (W. A. Benjamin, 1969).
- Faculty listing, Berkeley mathematics, retrieved 2011-04-09.
- Gannon, Terry (2006), Moonshine beyond the monster: the bridge connecting algebra, modular forms and physics, Cambridge monographs on mathematical physics, Cambridge University Press, p. 483, ISBN 978-0-521-83531-2, "In hindsight, the first incarnation of Monstrous Moonshine goes back to Andrew Ogg in 1975".
- Andrew Ogg at the Mathematics Genealogy Project