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

共 50 条

[1] ON ALGEBRAIC DIFFERENTIAL EQUATIONS OF GAMMA FUNCTION AND RIEMANN ZETA FUNCTION
Lu, Feng
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2019, 44 : 1031 - 1040
[2] 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
[3] Algebraic differential independence concerning the Euler Γ-function and Dirichlet series
Chen, Wei
Wang, Qiong
ACTA MATHEMATICA SCIENTIA, 2020, 40 (04) : 1035 - 1044
[4] 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
[5] On the Algebraic Difference Independence of the Euler Gamma Function G and Dirichlet Series
Li, Xiao-Min
Tahir, Hassan
Gao, Xue-Yuan
CONSTRUCTIVE APPROXIMATION, 2023, 58 (01) : 121 - 149
[6] ON ALGEBRAIC DIFFERENTIAL EQUATIONS FOR THE GAMMA FUNCTION AND L-FUNCTIONS IN THE EXTENDED SELBERG CLASS
Lu, Feng
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2017, 96 (01) : 36 - 43
[7] Algebraic differential equations with functional coefficients concerning ζ and Γ
Li, Bao Qin
Ye, Zhuan
JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (02) : 1456 - 1464
[8] 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
[9] 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
[10] On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations
Falkensteiner, Sebastian
Zhang, Yi
Vo, Thieu N.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (02)

← 1 2 3 4 5 →