On a relation between sums of arithmetical functions and dirichlet series

Hideaki Ishikawa*, Yuichi Kamiya

*この論文の責任著者

研究成果: ジャーナルへの寄稿学術論文査読

抄録

We introduce a concept called good oscillation. A function is called good oscillation, if its m-tuple integrals arbeounded 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 thesummatory functions of Dirichlet coefficients are good oscillation.

本文言語英語
ページ(範囲)97-105
ページ数9
ジャーナルPublications de l'Institut Mathematique
92
106
DOI
出版ステータス出版済み - 2012

ASJC Scopus 主題領域

  • 数学一般

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