On the Zeros of the Differential Polynomials φ f l ( f ( k ) ) n − a

Jiantang Lu and Junfeng Xu ()
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Jiantang Lu: School of Mathematics, Wuyi University, Jiangmen 529000, China
Junfeng Xu: School of Mathematics, Wuyi University, Jiangmen 529000, China

Mathematics, 2024, vol. 12, issue 8, 1-14

Abstract: Letting f be a transcendental meromorphic function, we consider the value distribution of the differential polynomials φ f l ( f ( k ) ) n − a , where φ ( ≢ 0 ) is a small function of f , l ( ≥ 2 ) , n ( ≥ 1 ) , k ( ≥ 1 ) are integers and a is a non-zero constant, and obtain an important inequality concerning the reduced counting function of φ f l ( f ( k ) ) n − a . Our results improve and generalize the results obtained by Xu and Ye, Karmakar and Sahoo, Chakraborty et.al, and Chen and Huang.

Keywords: meromorphic functions; differential polynomials; value distribution; small functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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