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arXiv · 2001.06250

On Petrenko's deviations and second order differential equations

J. Heittokangas·M. A. Zemirni
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Abstract

New results on the oscillation of solutions of $f''+A(z)f=0$ and on the growth of solutions of $f''+A(z)f'+B(z)f=0$ are obtained, where $A$ and $B$ are entire functions. Petrenko's magnitudes of deviation of $g$ with respect to $\infty$ play a key r\^ole in the results, where $g$ represents one of the coefficients $A$ or $B$. These quantities are defined by $\beta^-(\infty,g) = \liminf_{r\to\infty} \frac{\log M(r,g)}{T(r,g)}$ and $\beta^+(\infty,g) = \limsup_{r\to\infty} \frac{\log M(r,g)}{T(r,g)}$.

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J. Heittokangas, M. A. Zemirni. 2020-01-17. On Petrenko's deviations and second order differential equations. https://arxiv.org/abs/2001.06250

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