On zeros of solutions of higher order homogeneous linear differential equations

In this article, we investigate the exponent of convergence of zeros of solutions for some higher-order homogeneous linear differential equation, and prove that if Ak−1 is the dominant coefficient, then every transcendental solution f(z) of equation f(k)+Ak-1 f(k-1)+⋯+A0 f=0f(k)+Ak-1 f(k-1)+⋯+A0 f=0satisfies λ(f) = ∞, where λ(f) denotes the exponent of convergence of zeros of the meromorphic function f(z).