Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (2): 505-516.doi: 10.1007/s10473-021-0214-1

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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)

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

CLC Number: 

  • 34M15
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