Proceedings of the Japan Academy, Series A, Mathematical Sciences

Estimates of the proximate function of differential polynomials

Chung-Chun Yang and Zhuan Ye

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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.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 83, Number 4 (2007), 50-55.

First available in Project Euclid: 30 April 2007

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Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 30D35: Distribution of values, Nevanlinna theory 34M55: Painlevé and other special equations; classification, hierarchies;

Nevanlinna's value distribution theory differential polynomial Painlevé equations


Yang, Chung-Chun; Ye, Zhuan. Estimates of the proximate function of differential polynomials. Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 4, 50--55. doi:10.3792/pjaa.83.50.

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