Geodesic
On deviations from rational functions of entire functions of finite lower order
E. Ciechanowicz1 ; I. I. Marchenko1
1Department of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland
Annales Polonici Mathematici, Tome 91 (2007) no. 2-3, pp. 161-177
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Let $f$ be a transcendental entire function of finite lower order, and let $q_\nu$ be rational functions. For $0\gamma\infty\,$ let $$ B(\gamma):=\cases{ {\displaystyle\frac{\pi\gamma}{\sin\pi\gamma}}\hbox{if }\gamma\leq 0.5,\cr \pi\gamma\hbox{if }\gamma>0.5.\cr} $$ We estimate the upper and lower logarithmic density of the set $$ \Bigl\{r:\sum_{1\leq\nu\leq k}\log^+\max_{|z|=r}|f(z)-q_\nu(z)|^{-1} B(\gamma)T(r,f)\Bigr\}. $$
DOI : 10.4064/ap91-2-6
Keywords: transcendental entire function finite lower order rational functions gamma infty gamma cases displaystyle frac gamma sin gamma hbox gamma leq gamma hbox gamma estimate upper lower logarithmic density set bigl sum leq leq log max q gamma bigr

E. Ciechanowicz  1   ; I. I. Marchenko  1

1 Department of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland 
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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 91 (2007) no. 2-3, pp. 161-177. doi: 10.4064/ap91-2-6

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