Large deviations in Selberg's central limit theorem
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Following Selberg it is known that uniformly for V << (logloglog T)^{1/2 - \epsilon} the measure of those t \in [T;2T] for which log |\zeta(1/2 + it)| > V*((1/2)loglog T)^{1/2} is approximately T times the probability that a standard Gaussian random variable takes on values greater than V. We extend the range of V to V << (loglog T)^{1/10 - \epsilon}. We also speculate on the size of the largest V for which this normal approximation can hold and on the correct approximation beyond that point.
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Cited by 2 Pith papers
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Sharp Bounds for Moments of the Dedekind Zeta Function
Under GRH, upper bounds of conjectural order are proved for shifted moments of Dedekind zeta functions over finite Galois extensions, improving prior work.
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Conditional Upper Bounds for Large Deviations and Moments of the Riemann Zeta Function
Under RH, the measure of t in [T,2T] with |zeta(1/2+it)| > (log T)^k is <= C_k (log T)^{-k^2}/sqrt(log log T) with C_k=exp(e^{ck}), implying 2k-moment bounds C_k (log T)^{k^2}.
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