Algebraic differential independence regarding the Riemann ζ-function and the Euler Γ-function

被引：4

作者：

Han, Qi ^{[1
]}

Liu, Jingbo ^{[1
]}

机构：

[1] Texas A&M Univ, Dept Math, San Antonio, TX 78224 USA

来源：

JOURNAL OF NUMBER THEORY | 2021年 / 221卷

关键词：

Algebraic differential equations; The Riemann zeta-function; The Euler gamma-function; EQUATIONS;

D O I：

10.1016/j.jnt.2019.12.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove that zeta cannot be a solution to any nontrivial algebraic differential equation whose coefficients are polynomials in Gamma,Gamma((n)) and Gamma((ln)) over the ring of polynomials in C, where l, n >= 1 are positive integers. (c) 2020 Elsevier Inc. All rights reserved.

引用

页码：109 / 121

页数：13

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