Estimates of the proximate function of differential polynomials. (English) Zbl 1122.30022

Summary: We obtain a Clunie type theorem for a rather general form of functional equations involving differential polynomials. Our theorems can give a much sharper estimate on the error term of the proximity function of solutions of differential equations and functional equations than the upper bound obtained by Clunie, Doeringer, He-Xiao, Korhonen and etc. In particular, our theorem can also be applied to study various types of Painlevé differential equations.


30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
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