Ruprecht-Karls-Universität Heidelberg
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„Quantum Unique Ergodicity for holomorphic newforms“
Dr. Abhishek SAHA, University of Bristol

Recently, there has been a lot of interest in connections between quantum chaos and number theory. I will talk about the holomorphic quantum unique ergodicity conjecture and in particular, describe joint work with Paul Nelson and Ameya Pitale where we settle this conjecture in all aspects (for classical modular forms of trivial nebentypus). More precisely, let f be a classical holomorphic newform of level q and even weight k. 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). 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.

Donnerstag, den 8. November 2012 um 17 c.t. Uhr, in INF 288, HS2 Donnerstag, den 8. November 2012 at 17 c.t., in INF 288, HS2

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Kohnen