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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| Datum: | 1999 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1999
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4710 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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