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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A remark on distribution of zeros of solutions of linear differential equations


Author: Jian Hua Zheng
Journal: Proc. Amer. Math. Soc. 123 (1995), 847-854
MSC: Primary 34A20; Secondary 30C15
DOI: https://doi.org/10.1090/S0002-9939-1995-1233976-1
MathSciNet review: 1233976
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Abstract: The main purpose of this paper is to prove a sharp estimate of the order $ \rho (w)$ of a transcendental solution w in the complex plane of an n th-order linear differential equation with polynomial coefficients in terms of the distribution of its Stokes rays, under the assumption that zero is not a Nevanlinna deficient value of w. If, in addition, there are only two Stokes rays and if all the solutions of the equation have order at most $ \rho (w)$, then we can conclude that the coefficients of the equation are all constants.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1233976-1
Article copyright: © Copyright 1995 American Mathematical Society