I will discuss a variety of results on the fine-scale behavior of the real-analytic Eisenstein series on the modular surface SL_2(Z)\H. The study of eigenfunctions of the laplacian on a general hyperbolic surface has connections to mathematical physics, geometry, ergodic theory, etc. In the special arithmetic case of the modular surface, these questions have additional arithmetical content. In particular, many equidistribution properties of the Eisenstein series are related to mean values of the Riemann zeta function.
Tuesday, November 3rd, at 4:00pm in HBH 227
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