On the Differential and Difference Independence of Γ and ζ

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.

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Corresponding author

Correspondence to Qiong Wang.

Additional information

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)

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Chen, W., Wang, Q. On the Differential and Difference Independence of Γ and ζ. Acta Math Sci 41, 505–516 (2021). https://doi.org/10.1007/s10473-021-0214-1

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Key words

  • Algebraic differential equations
  • difference equations
  • the Euler gamma function
  • the Riemann zeta function

2010 MR Subject Classification

  • 34M15
  • 11M06
  • 33B15
  • 30D30