On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function

Qiongyan Wang, Manli Liu, Nan Li

In this paper, we prove that $\zeta$ is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in $\Gamma ,{\Gamma }^{(n)},{\Gamma }^{(l)}$ over the ring of p…