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Simon Marshall : L^p norms of arithmetic eigenfunctions

Let M be a compact Riemannian manifold, and f an L^2 normalised Laplace eigenfunction on M. A popular question in semiclassical analysis is how well one can bound the other L^p norms of f, or its restriction to a submanifold. I will give an introduction to this problem, and describe how one can make progress on it using the additional assumptions that M is arithmetic and f is a Hecke-Maass form.

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