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On the Algebraic Difference Independence of the Euler Gamma Function Γ and Dirichlet Series.
- Source :
-
Constructive Approximation . Aug2023, Vol. 58 Issue 1, p121-149. 29p. - Publication Year :
- 2023
-
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]
Details
- Language :
- English
- ISSN :
- 01764276
- Volume :
- 58
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Constructive Approximation
- Publication Type :
- Academic Journal
- Accession number :
- 171364066
- Full Text :
- https://doi.org/10.1007/s00365-022-09600-6