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

E. Ciechanowicz, I. I. Marchenko (2007)

Annales Polonici Mathematici

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 : 1 ν k l o g m a x | | z | | = r | f ( z ) q ν ( z ) | 1 < B ( γ ) T ( r , f ) .

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