PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 50(64) Preimenovati datoteke, proveriti paginaciju!!!, pp. 5159 (1991) 

Note on a paper by H.\,L. Montgomery ``Omega theorems for the Riemann zetafunction''K. Ramachandra and A. SankaranarayananSchool of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400\,005, IndiaAbstract: We study Omega theorems for the expression $E=\RE(e^{i\th} \log \zeta(\s_0+it_0))$ where $1/2\le\s_0<1$ and $0\le\th<2\pi$ ($\s_0$, $\th$ fixed) as $t_0\to\bb$. In fact we prove $E\ge C(1\s_0)^{1}(\log t_0)^{1\s_0} (\log\log t_0)^{\s_0}$ for at least one $t_0$ in $[T^{\e},T]$ where $C$ is a positive constant. Note that $(1\s_0)^{1}\to\bb$ as $\s_0\to1$. Keywords: Omega theorems, Riemann Zetafunction, Dirichlet box principle, Dedekind Zetafunction. Classification (MSC2000): 10H05 Full text of the article:
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