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

[21] Factorization of entire solutions of some algebraic differential equations
Wang, Xiaoling
Yang, Chung-Chun
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 324 (01) : 373 - 380
[22] Jacobi's bound for systems of algebraic differential equations
Kondratieva M.V.
Mikhalev A.V.
Pankratiev E.V.
Journal of Mathematical Sciences, 2009, 163 (5) : 543 - 553
[23] ON SOME PROPERTIES OF FIRST ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS
Yanchenko, A. Ya.
Podkopaeva, V. A.
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2019, 16 : 893 - 901
[24] Fixed points of the riemann zeta function and dirichlet series
Li, Bao Qin
Steuding, Joern
MONATSHEFTE FUR MATHEMATIK, 2022, 198 (03): : 581 - 589
[25] Alternating series in terms of Riemann zeta function and Dirichlet beta function
Fan, Zhiling
Chu, Wenchang
ELECTRONIC RESEARCH ARCHIVE, 2024, 32 (02): : 1227 - 1238
[26] Fixed points of the riemann zeta function and dirichlet series
Bao Qin Li
Jörn Steuding
Monatshefte für Mathematik, 2022, 198 : 581 - 589
[27] Some algebraic differential equations with few transcendental solutions
Gallagher, P. X.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 428 (02) : 717 - 734
[28] The class of solutions and algebraic integrability of algebraic differential equations. Trajectories of dynamical systems
Sobolevskii, SL
DIFFERENTIAL EQUATIONS, 2000, 36 (02) : 203 - 212
[29] The class of solutions and algebraic integrability of algebraic differential equations. trajectories of dynamical systems
S. L. Sobolevskii
Differential Equations, 2000, 36 : 203 - 212
[30] Algebraic differential independence regarding the Riemann ζ-function and the Euler Γ-function
Han, Qi
Liu, Jingbo
JOURNAL OF NUMBER THEORY, 2021, 221 : 109 - 121

← 1 2 3 4 5 →