论文标题
关于Riemann-Zeta函数和Euler-Gamma函数的代数微分方程
On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function
论文作者
论文摘要
在本文中，我们证明$ζ$不是解决任何非平凡代数差分方程的解决方案，其系数是$γ，γ^{（n）}，γ^{（n）}，γ^{（l）} $的多项式，$ \ \ \ \ \ mathbb {c} $，$ l> n becer in $ contyenmials in of doctionals。我们扩展了一个结果，即$ζ$不满足任何非平凡的代数微分方程，其系数是$γ，γ'，γ''$的多项式，这是li and ye [7]证明的。
In this paper, we prove that $ζ$ is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in $Γ, Γ^{(n)}, Γ^{(l)}$ over the ring of polynomials in $\mathbb{C}$, $l>n\geq 1$ are positive integers. We extended the result that $ζ$ does not satisfy any non-trivial algebraic differential equation whose coefficients are polynomials in $Γ, Γ', Γ''$ over the field of complex numbers, which is proved by Li and Ye[7].
