Three theorems concerning the exponent of convergence of the zero-sequence of solutions of where A is Entire

Abstract

In this paper, we investigate the distribution of zeros of solutions of

where A(z) is an entire function. Sufficient and necessary conditions are given here concerning the exponent of convergence of the zero-sequence of a solution in both cases where A(z) is a polynomial of degree n (where n is an even integer), and the case where A(z) is transcendental. In addition, we obtain one result of the following type: Let B(z) be a transcendental entire function of finite order, then for any two linearly independent solutions f ₁ f ₂ of (1) with .

AMS No.:

• 30 D15
• 34A20