Algebraic differential equations concerning the Riemann zeta function and the Euler gamma function Bao LiZhuan Ye 33B1512H0530D3534M15Riemann zeta functionEuler gamma functionalgebraic differential equation We prove that the Riemann zeta-function is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in $\Gamma$, $\Gamma'$ and $\Gamma''$ over the field of complex numbers. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3986 10.1512/iumj.2010.59.3986 en Indiana Univ. Math. J. 59 (2010) 1405 - 1416 state-of-the-art mathematics http://iumj.org/access/