Breadcrumb
Quantum Unique Ergodicity for holomorphic newforms
Wed 20 February 2013, 11:00
Abhishek Saha
Organiser: Tim Browning
ABSTRACT
Let f be a classical holomorphic newform of level q and even weight k. I will describe recent joint work with Paul Nelson and Ameya Pitale where we prove that the pushforward to the full level modular curve of the mass of f equidistributes as qk goes to infinity. This generalizes previous work by Holowinsky-Soundararajan (the case q=1, k-> infinity) and Nelson (the case qk -> infinity over squarefree integers q). Thus we settle the holomorphic quantum unique ergodicity conjecture in all aspects (for classical modular forms of trivial nebentypus). A potentially surprising aspect of our work is that we obtain a power savings in the rate of equidistribution as q becomes sufficiently ``powerful'' (far away from being squarefree), and in particular in the ``depth aspect'' as q traverses the powers of a fixed prime.