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
收藏
页码：109 / 121
页数：13
相关论文
共 50 条
[21]   Multitoric surfaces and Euler obstruction of a function [J].
Dalbelo, T. M. ;
Pereira, M. S. .
INTERNATIONAL JOURNAL OF MATHEMATICS, 2016, 27 (10)
[22]   SELF-APPROXIMATION FOR THE RIEMANN ZETA FUNCTION [J].
Nakamura, Takashi ;
Pankowski, Lukasz .
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2013, 87 (03) :452-461
[23]   Predicting transition with algebraic intermittency function [J].
Rahman, M. M. .
PHYSICS OF FLUIDS, 2022, 34 (03)
[24]   New Computations of the Riemann Zeta Function on the Critical Line [J].
Bober, Jonathan W. ;
Hiary, Ghaith A. .
EXPERIMENTAL MATHEMATICS, 2018, 27 (02) :125-137
[25]   Fourier Transforms of Positive Definite Kernels and the Riemann ξ-Function [J].
Csordas, George .
COMPUTATIONAL METHODS AND FUNCTION THEORY, 2015, 15 (03) :373-391
[26]   Fixed points of the riemann zeta function and dirichlet series [J].
Li, Bao Qin ;
Steuding, Joern .
MONATSHEFTE FUR MATHEMATIK, 2022, 198 (03) :581-589
[27]   FOURIER COEFFICIENTS ASSOCIATED WITH THE RIEMANN ZETA-FUNCTION [J].
Basiuk, Y., V ;
Tarasyuk, S., I .
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2016, 8 (01) :16-20
[28]   Fixed points of the riemann zeta function and dirichlet series [J].
Bao Qin Li ;
Jörn Steuding .
Monatshefte für Mathematik, 2022, 198 :581-589
[29]   ON THE MEAN SQUARE OF THE RIEMANN ZETA-FUNCTION IN SHORT INTERVALS [J].
Ivic, Aleksandar .
PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2009, 85 (99) :1-17
[30]   Integrability of and differential-algebraic structures for spatially 1D hydrodynamical systems of Riemann type [J].
Blackmore, Denis ;
Prykarpatsky, Yarema A. ;
Bogolubov, Nikolai N., Jr. ;
Prykarpatski, Anatolij K. .
CHAOS SOLITONS & FRACTALS, 2014, 59 :59-81
12345