Juan Rivera-Letelier, U Rochester
2:00 PM - 3:00 PM
Hylan 1106A and zoom id 566 385 6457 (no password)
A singular modulus is a value of the j-function at a quadratic imaginary number. These algebraic numbers lie at the heart of the theory of abelian extensions of imaginary quadratic fields. Recent work of Bilu, Habegger, Kuhne and Li shows that no singular modulus can be an algebraic unit. We show that for every finite set of prime numbers S, there is at most a finite number of singular moduli that are S-units. We will also discuss extensions of this result to other Hauptmoduln, including the Weber modular functions, the lambda-functions and the McKay-Thompson series associated with the elements of the monster group.
This is a joint work with Sebastian Herrero and Ricardo Menares.
Event contact: dinesh dot thakur at rochester dot edu