Abstract
We establish a relation between the lower bound for the maximum of the modulus of \(\zeta (1/2 + iT + s)\) in the disk \(|s| \leqslant H\) and the lower bound for the maximum of the modulus of \(\zeta (1/2 + iT + it)\) on the closed interval \(|t| \leqslant H\) for \(0 < H(T) \leqslant {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\). We prove a theorem on the lower bound for the maximum of the modulus of \(0 < H(T) \leqslant {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\) on the closed interval \(|t| \leqslant H\) for \(40 \leqslant H(T) \leqslant \log \log T\).
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Changa, M.E. Lower Bounds for the Riemann Zeta Function on the Critical Line. Mathematical Notes 76, 859–864 (2004). https://doi.org/10.1023/B:MATN.0000049686.37351.cb
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DOI: https://doi.org/10.1023/B:MATN.0000049686.37351.cb