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.

中文翻译：

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关于Γ和ζ的微分和差异独立性

在本文中，我们研究了Riemann zeta函数和Eulerγ函数之间的代数微分和差分独立性。证明Riemann zeta函数和Eulerγ函数不能满足一类非平凡的代数微分方程和代数差分方程。