Geodesic
An extension of Motohashi's observation on the zero-free region of the Riemann zeta-function
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 233-238

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We give an extension of Yoichi Motohashi's theorem saying that if the Riemann zeta-function on the line $\operatorname{Re}s=1$ attains very small values, then Vinogradov's zero-free region can be improved. 
@article{TM_2012_276_a18,
     author = {Sergei N. Preobrazhenskiǐ},
     title = {An extension of {Motohashi's} observation on the zero-free region of the {Riemann} zeta-function},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {233--238},
     publisher = {mathdoc},
     volume = {276},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_276_a18/}
}
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Sergei N. Preobrazhenskiǐ. An extension of Motohashi's observation on the zero-free region of the Riemann zeta-function. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 233-238. http://geodesic.mathdoc.fr/item/TM_2012_276_a18/