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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Proof of a conjecture of Bank and Laine regarding the product of two linearly independent solutions of $ y''+Ay=0$


Author: Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 100 (1987), 301-308
MSC: Primary 34A20; Secondary 30D35
MathSciNet review: 884470
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Abstract: Let $ A$ be a transcendental entire function of order $ < 1$. If $ {w_1}$ and $ {w_2}$ are two linearly independent solutions of the differential equation $ y'' + Ay = 0$, then at least one of $ {w_1},{w_2}$ has the property that the exponent of convergence of its zeros is $ > 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0884470-4
PII: S 0002-9939(1987)0884470-4
Keywords: Linearly independent solutions, entire functions, Cartan's lemma, Carleman's differential inequality
Article copyright: © Copyright 1987 American Mathematical Society