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An application of Borel-Carathéodory theorem. (English) Zbl 0685.30012

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 \(L(s, \chi)\)
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