Sums of Zeros of Solutions to Second Order Ode with Non-polynomial Coefficients

We consider the equation y′′ = F (z)y (z ∈ C) with an entire function F satisfying the condition |F (z)| ≤ A exp ` |z|ρ ρ ́ (ρ ≥ 1, A = const > 0). Let zk(y), k = 1, 2, . . . be the zeros of a solution y(z) to the above equation. Bounds for the sums j X k=1 1 |zk(y)| (j = 1, 2, . . . ) are established. Some applications of these bounds are also considered.