2012年
ON A RELATION BETWEEN SUMS OF ARITHMETICAL FUNCTIONS AND DIRICHLET SERIES
PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD
- ,
- 巻
- 92
- 号
- 106
- 開始ページ
- 97
- 終了ページ
- 108
- 記述言語
- 英語
- 掲載種別
- DOI
- 10.2298/PIM1206097I
- 出版者・発行元
- PUBLICATIONS L INSTITUT MATHEMATIQUE MATEMATICKI
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.
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.
- リンク情報
- ID情報
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- DOI : 10.2298/PIM1206097I
- ISSN : 0350-1302
- Web of Science ID : WOS:000312117200007