On deviations from rational functions of entire functions of finite lower order

E. Ciechanowicz; I. I. Marchenko

Annales Polonici Mathematici, Tome 92 (2007), p. 161-177 / Harvested from The Polish Digital Mathematics Library

Résumé

Let f be a transcendental entire function of finite lower order, and let $q_{ν}$ be rational functions. For 0 < γ < ∞ let B(γ):= πγ/sinπγ if γ ≤ 0.5, B(γ):= πγ if γ > 0.5. We estimate the upper and lower logarithmic density of the set $r : \sum_{1 \leq ν \leq k} l o g ⁺ m a x_{| | z | | = r} {| f (z) - q_{ν} (z) |}^{- 1} < B (γ) T (r, f)$ .

Publié le : 2007-01-01

Zbl 1201.30031

EUDML-ID : urn:eudml:doc:281065

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E. Ciechanowicz; I. I. Marchenko. On deviations from rational functions of entire functions of finite lower order. Annales Polonici Mathematici, Tome 92 (2007) pp. 161-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap91-2-6/