A limit theorem for Bohr – Jessen ’ s probability measures of the Riemann zeta-function

@inproceedings{Hattori2004ALT,
  title={A limit theorem for Bohr – Jessen ’ s probability measures of the Riemann zeta-function},
  author={Tetsuya Hattori},
  year={2004}
}
The asymptotic behavior of value distribution of the Riemann zeta-function ζ(s) is determined for 1 2 < (s) < 1. Namely, the existence is proved, and the value is given, of the limit lim →∞ ( (log )σ)−1/(1−σ) log W (C \ R( ), σ, ζ) for 1 2 < σ < 1, where R( ) is a square in the complex plane C of side length 2 centered at 0, and W (A,σ, ζ) = lim T→∞ (2T )−1μ1({t ∈ [−T, T ] | log ζ(σ + t √−1) ∈ A}) , A ⊂ C , where μ1 is the one-dimensional Lebesgue measure. Analogous results are obtained also… CONTINUE READING