On the growth of an entire dirichlet series
We establish the relation between the increase of the quantityM(σ,F) = ∣a 0∣ + ∑ n=1 ∞ ∣a n ∣ exp (σλ n ) and the behavior of sequences (|a n |) and (λ n ), where (λ n ) is a sequence of nonnegative numbers increasing to + ∞, andF(s) =a 0 + ∑ n=1 ∞ a n e sλn ,s=σ+it, is the Dirichlet entire...
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| Date: | 1999 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4710 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510874833256448 |
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| author | Sheremeta, M. M. Шеремета, М. М. |
| author_facet | Sheremeta, M. M. Шеремета, М. М. |
| author_sort | Sheremeta, M. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:11:43Z |
| description | We establish the relation between the increase of the quantityM(σ,F) = ∣a 0∣ + ∑ n=1 ∞ ∣a n ∣ exp (σλ n ) and the behavior of sequences (|a n |) and (λ n ), where (λ n ) is a sequence of nonnegative numbers increasing to + ∞, andF(s) =a 0 + ∑ n=1 ∞ a n e sλn ,s=σ+it, is the Dirichlet entire series. |
| first_indexed | 2026-03-24T03:03:56Z |
| format | Article |
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| id | umjimathkievua-article-4710 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:03:56Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a2/0f1fa3c4bbb14d9549bf2a8e07c2d6a2.pdf |
| spelling | umjimathkievua-article-47102020-03-18T21:11:43Z On the growth of an entire dirichlet series Про зростання цілого ряду Діріхле Sheremeta, M. M. Шеремета, М. М. We establish the relation between the increase of the quantityM(σ,F) = ∣a 0∣ + ∑ n=1 ∞ ∣a n ∣ exp (σλ n ) and the behavior of sequences (|a n |) and (λ n ), where (λ n ) is a sequence of nonnegative numbers increasing to + ∞, andF(s) =a 0 + ∑ n=1 ∞ a n e sλn ,s=σ+it, is the Dirichlet entire series. Вивчено зв'язок між зростанням величини $M(σ,F) = ∣a_0∣ + \sum_{n=1}^{ ∞} ∣a_n ∣ \exp (σλ_n )$ і поведінкою послідовностей $(|a_n|)$ та $(λ_n )$ ,де $(λ_n )$ — зростаюча до $+ ∞$ послідовність невід'ємних чисел, a $F(s) = a_0 + \sum_{n=1}^{ ∞} ∣a_n ∣ e^{sλn},\; s = σ + it$ —цілий ряд Діріхле. Institute of Mathematics, NAS of Ukraine 1999-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4710 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 8 (1999); 1149–1153 Український математичний журнал; Том 51 № 8 (1999); 1149–1153 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4710/6121 https://umj.imath.kiev.ua/index.php/umj/article/view/4710/6122 Copyright (c) 1999 Sheremeta M. M. |
| spellingShingle | Sheremeta, M. M. Шеремета, М. М. On the growth of an entire dirichlet series |
| title | On the growth of an entire dirichlet series |
| title_alt | Про зростання цілого ряду Діріхле |
| title_full | On the growth of an entire dirichlet series |
| title_fullStr | On the growth of an entire dirichlet series |
| title_full_unstemmed | On the growth of an entire dirichlet series |
| title_short | On the growth of an entire dirichlet series |
| title_sort | on the growth of an entire dirichlet series |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4710 |
| work_keys_str_mv | AT sheremetamm onthegrowthofanentiredirichletseries AT šeremetamm onthegrowthofanentiredirichletseries AT sheremetamm prozrostannâcílogorâdudíríhle AT šeremetamm prozrostannâcílogorâdudíríhle |