Lethbridge Number Theory and Combinatorics Seminar: Nathan Ng

Let f be a primitive modular form and L(s) its associated L-function. Anton Good (1982) bounded |L(s)| by approximately the cube root of the distance from the real axis on the line s = 1/2, in the case f is a modular form on the full modular group. In 1987, Matti Jutila gave a different proof and this was later refined by Martin Huxley. In this talk, we explain how the Jutila-Huxley approach can be generalized to the case of modular forms with arbitrary character X, weight k, and level N. This is joint work with Andrew Booker (Bristol) and Micah Milinovich (Mississippi).