Geodesic
Note on a Paper by h. l. Montgomery ``omega Theorems for the Riemann Zeta-function''
Publications de l'Institut Mathématique, _N_S_50 (1991) no. 64, p. 51
Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

We study Omega theorems for the expression $E=\text{Re}(e^{i\theta} \log \zeta(\sigma_0+it_0))$ where $1/2\le\sigma_01$ and $0\le\theta2\pi$ ($\sigma_0$, $\theta$ fixed) as $t_0\to\infty$. In fact we prove $E\ge C(1-\sigma_0)^{-1} (\log t_0)^{1-\sigma_0}(\log\log t_0)^{-\sigma_0}$ for at least one $t_0$ in $[T^{\varepsilon},T]$ where $C$ is a positive constant. Note that $(1-\sigma_0)^{-1}\to\bb$ as $\sigma_0\to1$.
Classification : 10H05
Keywords: Omega theorems, Riemann Zeta-function, Dirichlet box principle, Dedekind Zeta-function. 
@article{PIM_1991_N_S_50_64_a7,
     author = {K. Ramachandra and A. Sankaranarayanan},
     title = {Note on a {Paper} by h. l. {Montgomery} ``omega {Theorems} for the {Riemann} {Zeta-function''}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {51 },
     year = {1991},
     volume = {_N_S_50},
     number = {64},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1991_N_S_50_64_a7/}
}
TY  - JOUR
AU  - K. Ramachandra
AU  - A. Sankaranarayanan
TI  - Note on a Paper by h. l. Montgomery ``omega Theorems for the Riemann Zeta-function''
JO  - Publications de l'Institut Mathématique
PY  - 1991
SP  - 51 
VL  - _N_S_50
IS  - 64
UR  - http://geodesic.mathdoc.fr/item/PIM_1991_N_S_50_64_a7/
LA  - en
ID  - PIM_1991_N_S_50_64_a7
ER  - 
%0 Journal Article
%A K. Ramachandra
%A A. Sankaranarayanan
%T Note on a Paper by h. l. Montgomery ``omega Theorems for the Riemann Zeta-function''
%J Publications de l'Institut Mathématique
%D 1991
%P 51 
%V _N_S_50
%N 64
%U http://geodesic.mathdoc.fr/item/PIM_1991_N_S_50_64_a7/
%G en
%F PIM_1991_N_S_50_64_a7
K. Ramachandra; A. Sankaranarayanan. Note on a Paper by h. l. Montgomery ``omega Theorems for the Riemann Zeta-function''. Publications de l'Institut Mathématique, _N_S_50 (1991) no. 64, p. 51 . http://geodesic.mathdoc.fr/item/PIM_1991_N_S_50_64_a7/