The analytic properties of the Mellin transform of the second power of the ``short'' sum from the Riemann zeta-function approximate equation
Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 2, pp. 153-161
Voir la notice de l'article provenant de la source Math-Net.Ru
The approximate functional equation for $\left|\zeta\left(\dfrac{1}{2}+it\right)\right|^{2}$ ($t\gg 1$) is a sum of two sums and remainder. The first sum, called a “short” sum, contains $O(t^{2\varepsilon})$ terms, and the second sum contains $O(t^{2(1-\varepsilon)})$ terms ($0\varepsilon\frac12$). In this paper, we study analytic properties of the Mellin transform of the second power of the “short” sum absolute value and compare them with the corresponding properties of the Mellin transform of $\left|\zeta\left(\dfrac{1}{2}+it\right)\right|^{4}$.
@article{DVMG_2003_4_2_a0,
author = {L. V. Marchenko},
title = {The analytic properties of the {Mellin} transform of the second power of the ``short'' sum from the {Riemann} zeta-function approximate equation},
journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
pages = {153--161},
publisher = {mathdoc},
volume = {4},
number = {2},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a0/}
}
TY - JOUR AU - L. V. Marchenko TI - The analytic properties of the Mellin transform of the second power of the ``short'' sum from the Riemann zeta-function approximate equation JO - Dalʹnevostočnyj matematičeskij žurnal PY - 2003 SP - 153 EP - 161 VL - 4 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a0/ LA - ru ID - DVMG_2003_4_2_a0 ER -
%0 Journal Article %A L. V. Marchenko %T The analytic properties of the Mellin transform of the second power of the ``short'' sum from the Riemann zeta-function approximate equation %J Dalʹnevostočnyj matematičeskij žurnal %D 2003 %P 153-161 %V 4 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a0/ %G ru %F DVMG_2003_4_2_a0
L. V. Marchenko. The analytic properties of the Mellin transform of the second power of the ``short'' sum from the Riemann zeta-function approximate equation. Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 2, pp. 153-161. http://geodesic.mathdoc.fr/item/DVMG_2003_4_2_a0/