On a joint limit distribution for the Riemann zeta-function in the space of analytic functions
This paper is a continuation of the author's article [Lith. Math. J. 42, No. 3, 308-314 (2002; Zbl 1023.11041)], and the same applies for the reviews. The subject of this paper is the explicit form of the limit measure which was described in the paper and its review cited above. Denote by \(\gamma\) the unit circle in the complex plane, and define \(\Omega = \prod_{p}\gamma_{p}\) where the product is over all prime numbers and \(\gamma_{p} = \gamma\). Let \(\omega(p)\) stand for the projection of \(\omega\in \Omega\) onto \(\gamma_{p}\). Define on \((\Omega, \mathcal B (\Omega))\) the \(H^{r}(D)\)-valued random element \[ \zeta(s,\omega) = \Biggl( \prod_{p} \biggl(1-{\omega^{k_{1}}(p)\over p^{s}} \biggr)^{-1}, \ldots , \prod_{p} \biggl(1- {\omega^{k_{r}}(p)\over p^{s}}\biggr)^{-1}\Biggr). \] Then the distribution of \(\zeta(s,\omega)\), denoted by \(P_{\zeta}\), is the limit probability measure sought after.
scientific article; zbMATH DE number 1912635