On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane
For a Dirichlet series \(\sum\nolimits_{n = 1}^\infty {a_n \exp \{ s{\lambda}_n \} } \) with nonnegative exponents and zero abscissa of absolute convergence, we study the asymptotic behavior of the remainder \(\sum\nolimits_{k = n}^\infty {\left| {a_k } \right|\exp \{ {\delta \lambda}_k \} } \...
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| Date: | 2003 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3912 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510045427466240 |
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| author | Mikityuk, L. Ya. Sheremeta, M. M. Микитюк, Л. Я. Шеремета, М. М. |
| author_facet | Mikityuk, L. Ya. Sheremeta, M. M. Микитюк, Л. Я. Шеремета, М. М. |
| author_sort | Mikityuk, L. Ya. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:15:23Z |
| description | For a Dirichlet series \(\sum\nolimits_{n = 1}^\infty {a_n \exp \{ s{\lambda}_n \} } \) with nonnegative exponents and zero abscissa of absolute convergence, we study the asymptotic behavior of the remainder \(\sum\nolimits_{k = n}^\infty {\left| {a_k } \right|\exp \{ {\delta \lambda}_k \} } \) , δ < 0, as n → ∞. |
| first_indexed | 2026-03-24T02:50:45Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3912 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:50:45Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a9/6e321f73ce98f678f8cc50fc10ba1ba9.pdf |
| spelling | umjimathkievua-article-39122020-03-18T20:15:23Z On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane Про асимптотичну поведінку залишку абсолютно збіжного у півплощипі ряду Діріхле Mikityuk, L. Ya. Sheremeta, M. M. Микитюк, Л. Я. Шеремета, М. М. For a Dirichlet series \(\sum\nolimits_{n = 1}^\infty {a_n \exp \{ s{\lambda}_n \} } \) with nonnegative exponents and zero abscissa of absolute convergence, we study the asymptotic behavior of the remainder \(\sum\nolimits_{k = n}^\infty {\left| {a_k } \right|\exp \{ {\delta \lambda}_k \} } \) , δ < 0, as n → ∞. Для ряду Діріхле \(\sum\nolimits_{n = 1}^\infty {a_n \exp \{ s{\lambda}_n \} } \) з невід'ємними показниками і нульовою абсцисою абсолютної збіжності досліджено асимптотичну поведінку залишку | \(\sum\nolimits_{k = n}^\infty {\left| {a_k } \right|\exp \{ {\delta \lambda}_k \} } \) , δ < 0, при n → ∞. Institute of Mathematics, NAS of Ukraine 2003-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3912 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 3 (2003); 379-388 Український математичний журнал; Том 55 № 3 (2003); 379-388 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3912/4539 https://umj.imath.kiev.ua/index.php/umj/article/view/3912/4540 Copyright (c) 2003 Mikityuk L. Ya.; Sheremeta M. M. |
| spellingShingle | Mikityuk, L. Ya. Sheremeta, M. M. Микитюк, Л. Я. Шеремета, М. М. On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane |
| title | On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane |
| title_alt | Про асимптотичну поведінку залишку абсолютно
збіжного у півплощипі ряду Діріхле |
| title_full | On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane |
| title_fullStr | On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane |
| title_full_unstemmed | On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane |
| title_short | On the Asymptotic Behavior of the Remainder of a Dirichlet Series Absolutely Convergent in a Half-Plane |
| title_sort | on the asymptotic behavior of the remainder of a dirichlet series absolutely convergent in a half-plane |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3912 |
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