数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (2): 505-516.doi: 10.1007/s10473-021-0214-1

• 论文 • 上一篇    下一篇

ON THE DIFFERENTIAL AND DIFFERENCE INDEPENDENCE OF Γ AND ζ

陈玮, 王琼   

  1. School of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
  • 收稿日期:2020-02-07 修回日期:2020-05-18 出版日期:2021-04-25 发布日期:2021-04-29
  • 通讯作者: Qiong WANG E-mail:qiongwangsdu@126.com
  • 作者简介:Wei CHEN,E-mail:weichensdu@126.com
  • 基金资助:
    This work of both authors was partially supported by Basic and Advanced Research Project of CQ CSTC (cstc2019jcyj-msxmX0107), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202000621) and Fundamental Research Funds of Chongqing University of Posts and Telecommunications (CQUPT:A2018-125)

ON THE DIFFERENTIAL AND DIFFERENCE INDEPENDENCE OF Γ AND ζ

Wei CHEN, Qiong WANG   

  1. School of Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
  • Received:2020-02-07 Revised:2020-05-18 Online:2021-04-25 Published:2021-04-29
  • Contact: Qiong WANG E-mail:qiongwangsdu@126.com
  • About author:Wei CHEN,E-mail:weichensdu@126.com
  • Supported by:
    This work of both authors was partially supported by Basic and Advanced Research Project of CQ CSTC (cstc2019jcyj-msxmX0107), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202000621) and Fundamental Research Funds of Chongqing University of Posts and Telecommunications (CQUPT:A2018-125)

摘要: In this paper, we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function. It is proved that the Riemann zeta function and the Euler gamma function cannot satisfy a class of nontrivial algebraic differential equations and algebraic difference equations.

关键词: Algebraic differential equations, difference equations, the Euler gamma function, the Riemann zeta function

Abstract: In this paper, we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function. It is proved that the Riemann zeta function and the Euler gamma function cannot satisfy a class of nontrivial algebraic differential equations and algebraic difference equations.

Key words: Algebraic differential equations, difference equations, the Euler gamma function, the Riemann zeta function

中图分类号: 

  • 34M15