On algebraic differential properties of the Riemann ζ-function and the Euler Γ-function

We discuss some recent results on algebraic differential properties of the Riemann zeta-function and the Euler Gamma -function and prove two results in this direction. Especially, we will define a new class of meromorphic functions in terms of zeros of the Riemann zeta-function on the critical line and prove that algebraic equations with coefficients in this class cannot be satisfied by the Riemann zeta-function and the Euler Gamma-function.