1. On the Algebraic Difference Independence of the Euler Gamma Function Γ and Dirichlet Series.
- Author
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Li, Xiao-Min, Tahir, Hassan, and Gao, Xue-Yuan
- Subjects
DIRICHLET series ,GAMMA functions ,PERIODIC functions ,ALGEBRAIC equations ,ZETA functions ,DIFFERENTIAL equations - Abstract
We study the question of the algebraic difference independence of the Euler gamma function Γ and the functions in a certain class F , which contains those Dirichlet series as L-functions in the extended Selberg class S ♯ and some periodic functions. The main results in this paper are the difference analogues of the corresponding results from Lü (J Math Anal Appl 462(2):1195–1204, 2018) that showed that the Euler gamma function Γ and the functions in F can not satisfy a class of algebraic differential equations with meromorphic coefficients ϕ of Nevanlinna's characteristics satisfying T (r , ϕ) = o (r) , as r → ∞. Examples are provided to show that the main results in this paper, in a sense, are best possible. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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