Marchenko, I. I.; Shcherba, A. I. On the magnitudes of deviations of meromorphic functions. (Russian) Zbl 0697.30033 Mat. Sb. 181, No. 1, 3-24 (1990). Interesting results concerning defects in the Petrenko sense are proved in this paper. Among these results we mention the following ones. 1. Let f(z) be a meromorphic function in the complex plane, \(\lambda\) be its lower order, \[ \beta (\infty,f)=\liminf_{r\to \infty}(\max \{\log^+| f(z)|:\quad | z| =r\})/(T(r,f)), \] \(\beta\) (a,f)\(=\beta (\infty,(f-a)^{-1})\), \(a\in {\mathbb{C}}.\) Then \[ \sum_{a\in {\bar {\mathbb{C}}}}\beta (a,f)\leq 2\pi \lambda,\quad \lambda <1/2,\quad \sum_{a\in {\bar {\mathbb{C}}}}\beta (a,f)\leq (2\pi \lambda)/(\sin \pi \lambda),\quad \lambda \geq 1/2. \] 2. Define in the unit disk for the meromorphic function f(z) with unbounded characteristic T(r,f) \[ {\hat \beta}(\infty,f)=\liminf_{r\to \infty}((1-r)\max \{\log^+| f(z)|:\quad | z| =r\})/(T(r,f)). \] Then \({\hat \beta}\)(\(\infty,f)\leq \pi \lambda \cos^{-1-\lambda}(\pi /2(\lambda +1))\). The proofs use the technique of the *-function. Reviewer: M.Sodin Cited in 1 ReviewCited in 9 Documents MSC: 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory Keywords:*-function PDFBibTeX XMLCite \textit{I. I. Marchenko} and \textit{A. I. Shcherba}, Mat. Sb. 181, No. 1, 3--24 (1990; Zbl 0697.30033) Full Text: EuDML