关键词: 零点收敛指数, 复振荡, 超级, Borel方向.

Abstract:

In this paper, we investigate the distribution of zeros of solutions of second order differential equations f’’+A(z)f=0, where A(z) is an entire function of finite order. By using the Nevanlinna’s characteristic function and Ahlfors-Shimizu’s characteristic function on an angular domain, we established the existence of some ray which has the property that near which the exponent of convergence of the zero-sequence is infinite. Furthermore, by using a new method, we give a different proof of the Theorem 2 which has been given by Wu Shengjian in [5].

Key words: The exponent of convergence of the zero-sequence, Complex oscillation, Hyper order, Borel direction.