A study on algebraic differential equations of Gamma function and Dirichlet series

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Lu, Feng¹ 

[1] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China

关键词: The Riemann Zeta function;    The Gamma function;    Algebraic differential equation;   

DOI  :  10.1016/j.jmaa.2018.02.021

来源: Elsevier

【 摘 要 】

The paper concerns the problem of algebraic differential independence between the gamma function and the function in a certain class F, which contains Dirichlet L-functions, L-functions in the extended Selberg class and some periodic functions. It is proved that the gamma function and the function in F cannot satisfy a class of algebraic differential equations with meromorphic coefficients phi having Nevanlinna characteristic satisfying T(r, phi) = o(r) as r -> infinity. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free