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

共 16 条

[1] NOTE ON HOLDERS THEOREM CONCERNING GAMMA FUNCTION [J].

BANK, SB ;

KAUFMAN, RP .

MATHEMATISCHE ANNALEN, 1978, 232 (02) :115-120

[2] Some uniqueness results related to L-functions [J].

Han Q. .

Bollettino dell'Unione Matematica Italiana, 2017, 10 (4) :503-515

[3]

Hilbert D., 1902, Bull Amer. Math Soc, V8, P437, DOI DOI 10.1090/S0002-9904-1902-00923-3

[4]

Holder O, 1887, MATH ANN, V28, P1, DOI [10.1007/BF02430507, DOI 10.1007/BF02430507]

[5] Algebraic differential equations with functional coefficients concerning ζ and Γ [J].

Li, Bao Qin ;

Ye, Zhuan .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (02) :1456-1464

[6] Algebraic Differential Equations Concerning The Riemann Zeta Function and The Euler Gamma Function [J].

Li, Bao Qin ;

Ye, Zhuan .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2010, 59 (04) :1405-1415

[7]

Li BQ, 2010, P AM MATH SOC, V138, P2071

[8] On differential independence of the Riemann zeta function and the Euler gamma function [J].

Li, Bao Qin ;

Ye, Zhuan .

ACTA ARITHMETICA, 2008, 135 (04) :333-337

[9] Differential independence of Γ and ζ [J].

Markus, Lawrence .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2007, 19 (01) :133-154

[10]

Mordykhai-Boltovskoi D., 1914, Izv Politekh Inst Warsaw, V2, P1

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