Geodesic
Lower Bounds for the Riemann Zeta Function on the Critical Line
Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 922-927

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We establish a relation between the lower bound for the maximum of the modulus of $\zeta(1/2+iT+s)$ in the disk $|s|\le H$ and the lower bound for the maximum of the modulus of $\zeta(1/2+iT+it)$ on the closed interval $|t|\le H$ for $0$. We prove a theorem on the lower bound for the maximum of the modulus of $0$ on the closed interval $|t|\le H$ for $40\le H(T)\le\log\log T$. 
@article{MZM_2004_76_6_a12,
     author = {M. E. Changa},
     title = {Lower {Bounds} for the {Riemann} {Zeta} {Function} on the {Critical} {Line}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {922--927},
     publisher = {mathdoc},
     volume = {76},
     number = {6},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a12/}
}
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M. E. Changa. Lower Bounds for the Riemann Zeta Function on the Critical Line. Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 922-927. http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a12/