Open Access
April 2007 Estimates of the proximate function of differential polynomials
Chung-Chun Yang, Zhuan Ye
Proc. Japan Acad. Ser. A Math. Sci. 83(4): 50-55 (April 2007). DOI: 10.3792/pjaa.83.50


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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Chung-Chun Yang. Zhuan Ye. "Estimates of the proximate function of differential polynomials." Proc. Japan Acad. Ser. A Math. Sci. 83 (4) 50 - 55, April 2007.


Published: April 2007
First available in Project Euclid: 30 April 2007

zbMATH: 1122.30022
MathSciNet: MR2326202
Digital Object Identifier: 10.3792/pjaa.83.50

Primary: 14M25 , 30D35 , 34M55

Keywords: differential polynomial , Nevanlinna's value distribution theory , Painlevé equations

Rights: Copyright © 2007 The Japan Academy

Vol.83 • No. 4 • April 2007
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