Power Moments of the Error Term for the Approximate Functional Equation of the Riemann Zeta-function
Publications de l'Institut Mathématique, _N_S_52 (1992) no. 66, p. 10
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
Let $\zeta(s)$ be the Riemann zeta-function,
$d(n)$ the number of positive divisors of the integer $n$, and
$
R(s;t/2\pi) =\zeta^2(s) -\sum_{nłe t/2\pi}\!\!\!\strut'\enskip
d(n)n^{-s} -\chi^2(s) \sum_{nłe t/2\pi}\!\!\!\strut'\enskip d(n)n^{s-1},
$
where
$
\chi(s)=2^s\pi^{s-1}\sin(\frac12\pi s)\Gamma(1-s).
$
We obtain the following power moment estimates:
$
\int_1^T |R(\frac12+it;t/2\pi)|^A dt
łl \cases T^{1-\frac14A+\vaeepsilon},0łe Ałe4,\\ 1,>4.\endcases
$
Classification :
11M06
@article{PIM_1992_N_S_52_66_a2,
author = {Isao Kiuchi},
title = {Power {Moments} of the {Error} {Term} for the {Approximate} {Functional} {Equation} of the {Riemann} {Zeta-function}},
journal = {Publications de l'Institut Math\'ematique},
pages = {10 },
publisher = {mathdoc},
volume = {_N_S_52},
number = {66},
year = {1992},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1992_N_S_52_66_a2/}
}
TY - JOUR AU - Isao Kiuchi TI - Power Moments of the Error Term for the Approximate Functional Equation of the Riemann Zeta-function JO - Publications de l'Institut Mathématique PY - 1992 SP - 10 VL - _N_S_52 IS - 66 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/PIM_1992_N_S_52_66_a2/ LA - en ID - PIM_1992_N_S_52_66_a2 ER -
%0 Journal Article %A Isao Kiuchi %T Power Moments of the Error Term for the Approximate Functional Equation of the Riemann Zeta-function %J Publications de l'Institut Mathématique %D 1992 %P 10 %V _N_S_52 %N 66 %I mathdoc %U http://geodesic.mathdoc.fr/item/PIM_1992_N_S_52_66_a2/ %G en %F PIM_1992_N_S_52_66_a2
Isao Kiuchi. Power Moments of the Error Term for the Approximate Functional Equation of the Riemann Zeta-function. Publications de l'Institut Mathématique, _N_S_52 (1992) no. 66, p. 10 . http://geodesic.mathdoc.fr/item/PIM_1992_N_S_52_66_a2/