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Solution to a problem of S. Bank regarding exponent of convergence of zeros of the solutions of differential equation $$f''+Af=0$$. (English) Zbl 0636.34003
Consider the following differential equation (*) $$f''+Af=0$$ where A is a transcendental entire function of finite order. Let $$f_ 1$$ and $$f_ 2$$ be two linearly independent solutions of (*), then both $$f_ 1$$ and $$f_ 2$$ are entire functions. S. Bank and I. Laine proved the following theorem: If the order of A is less than 1/2, then at least one of $$f_ 1$$, $$f_ 2$$ has the property that the exponent of convergence of its zeros is $$\infty$$ [Trans. Am. Math. Soc. 273, 351-363 (1982; Zbl 0505.34026]. It is shown that the conclusion of the above theorem holds if the order of A is less than or equal to 1/2.
Reviewer: K.Takano

##### MSC:
 34M99 Ordinary differential equations in the complex domain 34A30 Linear ordinary differential equations and systems, general