Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation
Let M f(r) and μ f (r) be, respectively, the maximum of the modulus and the maximum term of an entire function f and let l(r) be a continuously differentiable function convex with respect to ln r. We establish that, in order that ln M f(r) ∼ ln μ f (r), r → +∞, for every entire function f such that...
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4273 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | Let M f(r) and μ f (r) be, respectively, the maximum of the modulus and the maximum term of an entire function f and let l(r) be a continuously differentiable function convex with respect to ln r. We establish that, in order that ln M f(r) ∼ ln μ f (r), r → +∞, for every entire function f such that μ f (r) ∼ l(r), r → +∞, it is necessary and sufficient that ln (rl′(r)) = o(l(r)), r → +∞. |
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