Lethbridge Number Theory and Combinatorics Seminar: Nathan Ng

Let $L(s)$ be the $L$-function associated to a modular form of weight $k$ for the full modular group.

Using spectral theory, Anton Good proved that $L(k/2+it) \ll t^{1/6} (\log t)^{5/6}$.  Matti Jutila discovered a simpler proof which makes use of the Voronoi summation formula, exponential integrals, and Farey fractions. We shall present Jutila's argument.