On the location of zeros of solutions of non-homogeneous linear differential equations (Q1891523)

The nonhomogeneous linear differential equation of arbitrary order (1) \(w^{(n)} + R_{n - 1} (z)w^{(n - 1)} + \cdots + R(z)w = Q(z)\) in the complex domain is considered. The coefficients \(R_i\) in (1) are rational functions. Precisely those rays \(\text{Arg} z = \varphi\) which have the property that for any \(\varepsilon > 0\), there is a solution of (1) which has infinitely many zeros tending to \(\infty\) in the sector \(|\text{Arg} z - \varphi |< \varepsilon\) are determined. The results represent certain generalization of the earlier ones for (1) with polynomial coefficients and \(Q(Z) = 0\). The author actually treats equations (1) whose coefficients belong to a certain type of function field.