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

被引：8

作者：

Lu, Feng ^{[1
]}

机构：

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 462卷 / 02期

关键词：

The Riemann Zeta function; The Gamma function; Algebraic differential equation; RIEMANN ZETA-FUNCTION; INDEPENDENCE;

D O I：

10.1016/j.jmaa.2018.02.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：1195 / 1204

页数：10

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