Geodesic
On a Relation Between Sums of Arithmetical Functions and Dirichlet Series
Publications de l'Institut Mathématique, _N_S_92 (2012) no. 106, p. 97 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We introduce a concept called good oscillation. A function is called good oscillation, if its $m$-tuple integrals are bounded by functions having mild orders. We prove that if the error terms coming from summatory functions of arithmetical functions are good oscillation, then the Dirichlet series associated with those arithmetical functions can be continued analytically over the whole plane. We also study a sort of converse assertion that if the Dirichlet series are continued analytically over the whole plane and satisfy a certain additional assumption, then the error terms coming from the summatory functions of Dirichlet coefficients are good oscillation.
Classification : 11M06
Keywords: arithmetical function, Dirichlet series, analytic continuation 
@article{PIM_2012_N_S_92_106_a6,
     author = {Hideaki Ishikawa and Yuichi Kamiya},
     title = {On a {Relation} {Between} {Sums} of {Arithmetical} {Functions} and {Dirichlet} {Series}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {97 },
     publisher = {mathdoc},
     volume = {_N_S_92},
     number = {106},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2012_N_S_92_106_a6/}
}
TY  - JOUR
AU  - Hideaki Ishikawa
AU  - Yuichi Kamiya
TI  - On a Relation Between Sums of Arithmetical Functions and Dirichlet Series
JO  - Publications de l'Institut Mathématique
PY  - 2012
SP  - 97 
VL  - _N_S_92
IS  - 106
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PIM_2012_N_S_92_106_a6/
LA  - en
ID  - PIM_2012_N_S_92_106_a6
ER  - 
%0 Journal Article
%A Hideaki Ishikawa
%A Yuichi Kamiya
%T On a Relation Between Sums of Arithmetical Functions and Dirichlet Series
%J Publications de l'Institut Mathématique
%D 2012
%P 97 
%V _N_S_92
%N 106
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PIM_2012_N_S_92_106_a6/
%G en
%F PIM_2012_N_S_92_106_a6
Hideaki Ishikawa; Yuichi Kamiya. On a Relation Between Sums of Arithmetical Functions and Dirichlet Series. Publications de l'Institut Mathématique, _N_S_92 (2012) no. 106, p. 97 . http://geodesic.mathdoc.fr/item/PIM_2012_N_S_92_106_a6/