SeminarsRandom Matrices, Strong Szegö's theorem and L functions
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Fluctuations of random matrix theory type have been known to occur in analytic number theory since Montgomery's calculation of the pair correlation of the zeta zeros, in the microscopic regime. At the mesoscopic scale, the analogy still holds, through a limiting Gaussian field, which presents an ultrametric structure similar to Coulomb gases. In particular we will present an unconditional proof for the analogue of the strong Szegö theorem, for L-functions in the Selberg class. This talk is based on work with Jeffrey Kuan (Harvard).
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Paul Bourgade
2013-07-02
10:30:00 - 12:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
Fluctuations of random matrix theory type have been known to occur in analytic number theory since Montgomery's calculation of the pair correlation of the zeta zeros, in the microscopic regime. At the mesoscopic scale, the analogy still holds, through a limiting Gaussian field, which presents an ultrametric structure similar to Coulomb gases. In particular we will present an unconditional proof for the analogue of the strong Szegö theorem, for L-functions in the Selberg class. This talk is based on work with Jeffrey Kuan (Harvard).