On algebraic differential properties of the Riemann ζ-function and the Euler Γ-function

被引：11

作者：

Li, B. Q. ^{[1
]}

Ye, Z. ^{[2
]}

机构：

[1] Florida Int Univ, Dept Math, Miami, FL 33199 USA

[2] No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2011年 / 56卷 / 1-4期

关键词：

The Riemann zeta-function; the Euler Gamma-function; polynomial; algebraic differential equation; INDEPENDENCE;

D O I：

10.1080/17476930903394788

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss some recent results on algebraic differential properties of the Riemann zeta-function and the Euler Gamma -function and prove two results in this direction. Especially, we will define a new class of meromorphic functions in terms of zeros of the Riemann zeta-function on the critical line and prove that algebraic equations with coefficients in this class cannot be satisfied by the Riemann zeta-function and the Euler Gamma-function.

引用

页码：137 / 145

页数：9

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