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Title:
Large deviation estimates for Selberg’s central limit theorem and applications
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Abstract:
Selberg’s central limit theorem gives that the logarithm of the Riemann zeta function taken at a uniformly drawn height in $[T, 2T]$ behaves as a complex centered Gaussian random variable with variance $\log\log T$. A natural question is to investigate how far the Gaussian decay persists. We present results on the right tail for the real part of the logarithm, where the absolute value of zeta is `unusually large’, on the scale of the exponential of the variance. The result is in agreement with the corresponding (known) random matrix result, under the usual dictionary. This work is joint with Louis-Pierre Arguin.
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