On the Binomial Asymptotics of an Entire Dirichlet Series
Let M(σ) be the maximum modulus and let μ(σ) be the maximum term of an entire Dirichlet series with nonnegative exponents λ n increasing to ∞. We establish a condition for λ n under which the relations $$\ln {\mu }\left( {{\sigma ,}F} \right) \leqslant \Phi _1 \left( {\sigma } \right) + \left( {...
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| Datum: | 2001 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2001
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4275 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Let M(σ) be the maximum modulus and let μ(σ) be the maximum term of an entire Dirichlet series with nonnegative exponents λ n increasing to ∞. We establish a condition for λ n under which the relations $$\ln {\mu }\left( {{\sigma ,}F} \right) \leqslant \Phi _1 \left( {\sigma } \right) + \left( {1 + o\left( 1 \right)} \right){\tau }\Phi _{2} \left( {\sigma } \right)\quad \left( {{\sigma } \to + \infty } \right)$$ and $$\ln M\left( {{\sigma ,}F} \right) \leqslant \Phi _1 \left( {\sigma } \right) + \left( {1 + \left( 1 \right)} \right){\tau }\Phi _{2} \left( {\sigma } \right)\quad \left( {{\sigma } \to + \infty } \right)$$ are equivalent under certain conditions on the functions Φ1 and Φ2. |
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