On the Functional Independence of the Riemann Zeta-Function

被引：1

作者：

Garbaliauskiene, Virginija ^{[1
]}

Macaitiene, Renata ^{[2
]}

Siauciunas, Darius ^{[2
]}

机构：

[1] Siauliai State Univ Appl Sci, Fac Business & Technol, Ausros Al 40, LT-76241 Shiauliai, Lithuania

[2] Vilnius Univ, Inst Reg Dev, Siauliai Acad, P Visinskio G 25, LT-76153 Shiauliai, Lithuania

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2023年 / 28卷 / 02期

关键词：

functional independence; Riemann zeta-function; universality of zeta-functions; JOINT VALUE-DISTRIBUTION; UNIVERSALITY;

D O I：

10.3846/mma.2023.17157

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1973, Voronin proved the functional independence of the Riemann zeta-function zeta (s), i.e., that zeta(s) and its derivatives do not satisfy a certain equation with continuous functions. In the paper, we obtain a joint version of the Voronin theorem.

引用

页码：352 / 359

页数：8

共 50 条

[41] ON SOME PROBLEMS IN THE THEORY OF RIEMANN ZETA-FUNCTION
Korobeinik, Yu. F.
UFA MATHEMATICAL JOURNAL, 2015, 7 (04): : 88 - 93
[42] Some identities related to Riemann zeta-function
Lin Xin
Journal of Inequalities and Applications, 2016
[43] Several identities relating to Riemann zeta-Function
Wu, Zhengang
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2016, 59 (03): : 285 - 294
[44] Some identities related to Riemann zeta-function
Xin, Lin
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, : 1 - 6
[45] Discrete Schwartz distributions and the Riemann zeta-function
Florin Nicolae
Alberto Verjovsky
Bulletin of the Brazilian Mathematical Society, New Series, 2010, 41 : 211 - 221
[46] About Riemann's Zeta-Function and Applications
Daili, Noureddine
COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2020, 11 (03): : 461 - 479
[47] Shifted fourth moment of the Riemann zeta-function
Shimomura, S.
ACTA MATHEMATICA HUNGARICA, 2012, 137 (1-2) : 104 - 129
[48] Shifted fourth moment of the Riemann zeta-function
Shun Shimomura
Acta Mathematica Hungarica, 2012, 137 : 104 - 129
[49] Approximation by generalized shifts of the Riemann zeta-function in short intervals
Antanas Laurinčikas
The Ramanujan Journal, 2021, 56 : 309 - 322
[50] Difference independence of the Riemann zeta function
Chiang, Yik-Man
Feng, Shao-Ji
ACTA ARITHMETICA, 2006, 125 (04) : 317 - 329

← 1 2 3 4 5 →