Large deviations in Selberg's central limit theorem
Number Theory
2011-08-26 v1 Probability
Abstract
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.
Cite
@article{arxiv.1108.5092,
title = {Large deviations in Selberg's central limit theorem},
author = {Maksym Radziwill},
journal= {arXiv preprint arXiv:1108.5092},
year = {2011}
}
Comments
9 pages