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A limit theorem for the Riemann zeta-function close to the critical line
Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 1-9 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that as $T\to\infty$ the distribution function $$ \frac1T\operatorname{mes}\{t\in[0,T],\ |\zeta(\sigma_T+it)|^\frac{1}{\sqrt{2^{-1}\ln\ln T}}<x\} $$ approaches the distribution function of the logarithmic normal distribution. Here $\operatorname{mes}\{A\}$ is the Lebesgue measure of the set $A$, and $$ \sigma_T=\frac12+\frac{\sqrt{\ln\ln T}\psi(T)}{\ln T}, $$ where $\psi(T)\to\infty$ and $\ln\psi(T)=o(\ln\ln T)$ as $T\to\infty$. Bibliography: 11 titles. 
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A. P. Laurincikas. A limit theorem for the Riemann zeta-function close to the critical line. Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 1-9. http://geodesic.mathdoc.fr/item/SM_1989_63_1_a0/

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