The unbounded denominators conjecture

Abstract: The unbounded denominators conjecture, first raised by Atkin and Swinnerton-Dyer, asserts that a modular form for a finite index subgroup of $\SL_2(\mathbb Z)$ whose Fourier coefficients have bounded denominators must be a modular form for some congruence subgroup. In this talk, we will give a sketch of the proof of this conjecture based on a new arithmetic algebraization theorem. This is joint work with Frank Calegari and Vesselin Dimitrov.

number theory

Audience: researchers in the topic

Harvard number theory seminar