On the Connection between the Nevanlinna Characteristics of an Entire Function and of its Derivative

Julian Ławrynowicz and Sakari Toppila
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Julian Ławrynowicz: Polish Academy of Sciences, Institute of Mathematics
Sakari Toppila: University of Helsinki, Department of Mathematics

A chapter in Deformations of Mathematical Structures, 1989, pp 51-53 from Springer

Abstract: Abstract We use the usual notation of the Nevanlinna theory. The following result is mentioned but not proved in [2]: There exists an absolute constant Q > 1 such that 1 $$\mathop{{\lim sup}}\limits_{{{{r}^{{ \to \infty }}}}} [T(Qr,f\prime )/T(r,f)] \geqslant 1$$ for any transcendental entire function f. Now we give a numerical estimate for the constant Q. We prove that if f is a transcendental entire function then 2 $$ {\lim_{{r \to \infty }}}\sup [T(10r,{f^{'}})/T(r,f)] \geqslant 1 $$

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-2643-1_5

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DOI: 10.1007/978-94-009-2643-1_5

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