Analytic Aspects of L-functions and Related Problems

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This proposal is centered on new approaches to tackle problems concerning analytic aspects of automorphic L-functions, and their intrinsic connnection to various equidistribution problems in Number Theory, especially the quantitative and effective results in the mass equidistribution properties of Hecke eigenforms on arithmetic surfaces, as well as its higher dimensional generalizations. The equidistribution problems have their origin from mathematical physics and quantum mechanics, and are well connected to other major areas in mathematics. The rich interplay and interaction of ideas across different fields lie at the heart of the current project.Because of these distinctive features the research project proposed here are also ideal for training and engaging postdoctoral researchers and Ph.D. students in a vibrant and important research area.