Mod-Gaussian convergence and the value distribution of $ζ(1/2+it)$ and related quantities

Details Mod-Gaussian convergence and the value distribution of $ζ(1/2+it)$ and related quantities Mod-Gaussian convergence and the value distribution of $ζ(1/2+it)$ and related quantities

2009-12-16

arxiv.org/abs/0912.3237v3

Mathematics

Number Theory

26 pages, 2 figures, v3: stronger quantitative statements and other changes

Scientific paper

In the context of mod-Gaussian convergence, as defined previously in our work with J. Jacod, we obtain lower bounds for local probabilities for a sequence of random vectors which are approximately Gaussian with increasing covariance. This is motivated by the conjecture concerning the density of the set of values of the Riemann zeta function on the critical line. We obtain evidence for this fact, and derive unconditional results for random matrices in compact classical groups, as well as for certain families of L-functions over finite fields.

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