Illinois Journal of Mathematics

When an entire function and its linear differential polynomial share two values

Ping Li and Chung-Chun Yang

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Abstract

In this note, the relationship between a non-constant entire function $f$ and its linear differential polynomial $L(f)$ has been obtained when they share two finite values, ignoring multiplicities, by applying value distribution theory. This confirms Frank's conjecture as a special case. Entire solutions of certain types of non-linear differential equations are also discussed.

Article information

Source
Illinois J. Math., Volume 44, Issue 2 (2000), 349-362.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255984845

Digital Object Identifier
doi:10.1215/ijm/1255984845

Mathematical Reviews number (MathSciNet)
MR1775326

Zentralblatt MATH identifier
0958.30016

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory
Secondary: 30D20: Entire functions, general theory

Citation

Li, Ping; Yang, Chung-Chun. When an entire function and its linear differential polynomial share two values. Illinois J. Math. 44 (2000), no. 2, 349--362. doi:10.1215/ijm/1255984845. https://projecteuclid.org/euclid.ijm/1255984845


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