Mod-Gaussian convergence and the value distribution of ζ(½ + it) and related quantities

@article{Kowalski2012ModGaussianCA,
  title={Mod-Gaussian convergence and the value distribution of ζ(½ + it) and related quantities},
  author={E. Kowalski and A. Nikeghbali},
  journal={J. Lond. Math. Soc.},
  year={2012},
  volume={86},
  pages={291-319}
}
  • E. Kowalski, A. Nikeghbali
  • Published 2012
  • Mathematics, Computer Science
  • J. Lond. Math. Soc.
  • In the context of mod-Gaussian convergence, as defined previously in our work with Jacod, we obtain asymptotic formulas and lower bounds for local probabilities for a sequence of random vectors which are approximately Gaussian in this sense, with increasing covariance matrix. 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… CONTINUE READING
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    References

    SHOWING 1-10 OF 42 REFERENCES
    Random Matrix Theory and ζ(1/2+it)
    • 593
    • Highly Influential
    • PDF
    On the Riemann zeta-function—Mean value theorems and the distribution of |S(T)|
    • 48
    • Highly Influential
    Random Matrix Theory and L-Functions at s= 1/2
    • 265
    • Highly Influential
    • PDF
    SATO-TATE THEOREMS FOR MELLIN TRANSFORMS OVER FINITE FIELDS
    • 2
    Eigenvalue distributions of random unitary matrices
    • 48