Subconvex equidistribution of cusp forms
Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017
Arithmetic Quantum Chaos
arithmetic quantum unique ergodicity
11F70 - Representation-theoretic methods; automorphic representations over local and global fields
11F27 - Theta series; Weil representation; theta correspondences
58J51 - Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
11F67 - Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Arithmetic quantum chaos concerns the limiting behavior of a sequence of automorphic forms with parameters tending off to infinity. It is now known in many cases that the mass distributions of such forms equidistribute. Unfortunately, the known rates of equidistribution are typically weak (ineffective or logarithmic). I will discuss the problem of obtaining strong rates (power savings) and the related subconvexity problem, emphasizing recent progress concerning the level aspect on hyperbolic surfaces.
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