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

被引：2

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

共 50 条

[1] RESULTS ON THE ALGEBRAIC DIFFERENTIAL INDEPENDENCE OF THE RIEMANN ZETA FUNCTION AND THE EULER GAMMA FUNCTION
Li, Xiao-min
Li, Yi-xuan
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2023, 60 (06) : 1651 - 1672
[2] On algebraic differential properties of the Riemann ζ-function and the Euler Γ-function
Li, B. Q.
Ye, Z.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2011, 56 (1-4) : 137 - 145
[3] On differential independence of the Riemann zeta function and the Euler gamma function
Li, Bao Qin
Ye, Zhuan
ACTA ARITHMETICA, 2008, 135 (04) : 333 - 337
[4] Algebraic Differential Equations Concerning The Riemann Zeta Function and The Euler Gamma Function
Li, Bao Qin
Ye, Zhuan
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2010, 59 (04) : 1405 - 1415
[5] Algebraic differential independence concerning the Euler Γ-function and Dirichlet series
Chen, Wei
Wang, Qiong
ACTA MATHEMATICA SCIENTIA, 2020, 40 (04) : 1035 - 1044
[6] Algebraic differential independence concerning the Euler Γ-function and Dirichlet series
Wei Chen
Qiong Wang
Acta Mathematica Scientia, 2020, 40 : 1035 - 1044
[7] ALGEBRAIC DIFFERENTIAL INDEPENDENCE CONCERNING THE EULER Γ-FUNCTION AND DIRICHLET SERIES
陈玮
王琼
ActaMathematicaScientia, 2020, 40 (04) : 1035 - 1044
[8] On the Difference Independence of the Euler Gamma Function and the Riemann Zeta Function
Bibi, Amina
Li, Xiao-Min
Yi, Hong-Xun
COMPUTATIONAL METHODS AND FUNCTION THEORY, 2023, 23 (04) : 771 - 788
[9] On the Difference Independence of the Euler Gamma Function and the Riemann Zeta Function
Amina Bibi
Xiao-Min Li
Hong-Xun Yi
Computational Methods and Function Theory, 2023, 23 : 771 - 788
[10] On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function
Wang, Qiongyan
Li, Zhi
Liu, Manli
Li, Nan
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2022, 67 (10) : 2507 - 2518

← 1 2 3 4 5 →