This article is cited in 8 papers

Lower Bounds for the Riemann Zeta Function on the Critical Line

M. E. Changa

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We establish a relation between the lower bound for the maximum of the modulus of $\zeta(1/2+iT+s)$ in the disk $|s|\le H$ and the lower bound for the maximum of the modulus of $\zeta(1/2+iT+it)$ on the closed interval $|t|\le H$ for $0<H(T)\le1/2$. We prove a theorem on the lower bound for the maximum of the modulus of $0<H(T)\le1/2$ on the closed interval $|t|\le H$ for $40\le H(T)\le\log\log T$.

UDC: 511

Received: 30.06.2004

DOI: 10.4213/mzm151

 English version: Mathematical Notes, 2004, 76:6, 859–864

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