Ramachandra, K. An application of Borel-Carathéodory theorem. (English) Zbl 0685.30012 J. Ramanujan Math. Soc. 4, No. 1, 45-52 (1989). Some applications of the well-known Borel-Carathéodory theorem are given. These results are applied to prove some \(\Omega\)-results in the theory of the Riemann zeta-function. An open question raised by the author is “prove or disprove that \(Re \zeta (1+it)=\Omega_-(\log \log t)''.\) Reviewer: K.Ramachandra MSC: 30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 11M06 \(\zeta (s)\) and \(L(s, \chi)\) Keywords:maximum modulus principle; Borel-Carathéodory theorem; \(\Omega\)- results; Riemann zeta-function PDFBibTeX XMLCite \textit{K. Ramachandra}, J. Ramanujan Math. Soc. 4, No. 1, 45--52 (1989; Zbl 0685.30012)