Ramachandra, K.; Sankaranarayanan, A. Note on a paper by H. L. Montgomery (Omega theorems for the Riemann zeta- function). (English) Zbl 0743.11044 Publ. Inst. Math., Nouv. Sér. 50(64), 51-59 (1991). It is proved unconditionally that if \(\theta\) is fixed and \({1\over 2}<\sigma<1\) then \[ \hbox{Re}(e^{-i\theta}\log\zeta(\sigma+it))\geq C(\sigma)(\log t)^{1-\sigma}(\log\log t)^{-\sigma} \] for a sequence of arbitrarily large values of \(t\). Here \(C(\sigma)\gg 1/(1-\sigma)\) is an explicitly given constant, and one aim of the paper is to obtain as large a value as possible. On the Riemann Hypothesis a corresponding result for \(\sigma={1\over 2}\) is obtained. The authors follow the method used by H. L. Montgomery [Comment. Math. Helv. 52, 511-518 (1977; Zbl 0373.10024)]. Reviewer: D.R.Heath-Brown (Oxford) Cited in 3 Documents MSC: 11M06 \(\zeta (s)\) and \(L(s, \chi)\) 11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses Keywords:Riemann zeta-function; Omega theorems; critical strip; logarithm; Riemann Hypothesis Citations:Zbl 0373.10024 PDFBibTeX XMLCite \textit{K. Ramachandra} and \textit{A. Sankaranarayanan}, Publ. Inst. Math., Nouv. Sér. 50(64), 51--59 (1991; Zbl 0743.11044) Full Text: EuDML