Subconvex equidistribution of cusp forms
Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017
Arithmetic Quantum Chaos
Automorphic forms
arithmetic quantum unique ergodicity
subconvexity bound
L-function
11H31 - Lattice packing and covering (number-theoretic aspects) [See also 05B40, 52C15, 52C17]
11G18 - Arithmetic aspects of modular and Shimura varieties [See also 14G35]
11G20 - Curves over finite and local fields [See also 14H25]
11H06 - Lattices and convex bodies (number-theoretic aspects) [See also 11P21, 52C05, 52C07]
Nelson
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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