LAUSR

Abstract. Due to Voronin’s universality theorem and Riemann–von Mangoldt formula, this paper concerns the problem of algebraic differential independence between the gamma function Γ and the function f(ζ), where ζ is the Riemann zeta function and f is a function with at least one zero-point. It is showed that Γ and f(ζ) cannot satisfy any nontrivial distinguished differential equation with meromorphic coefficients φ having Nevanlinna characteristic satisfying T (r, φ) = o(r) as r → ∞.