Proof of a conjecture of Bank and Laine regarding the product of two linearly independent solutions of $y”+Ay=0$
HTML articles powered by AMS MathViewer
- by Li-Chien Shen PDF
- Proc. Amer. Math. Soc. 100 (1987), 301-308 Request permission
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 $> 1$.References
- Kihachiro Arima, On maximum modulus of integral functions, J. Math. Soc. Japan 4 (1952), 62–66. MR 49320, DOI 10.2969/jmsj/00410062
- Steven B. Bank and Ilpo Laine, On the oscillation theory of $f^{\prime \prime }+Af=0$ where $A$ is entire, Trans. Amer. Math. Soc. 273 (1982), no. 1, 351–363. MR 664047, DOI 10.1090/S0002-9947-1982-0664047-6
- Steven B. Bank and Ilpo Laine, On the zeros of meromorphic solutions and second-order linear differential equations, Comment. Math. Helv. 58 (1983), no. 4, 656–677. MR 728459, DOI 10.1007/BF02564659 A. Edrei, The problem of Bank and Laine, unpublished manuscript.
- B. Ja. Levin, Distribution of zeros of entire functions, Revised edition, Translations of Mathematical Monographs, vol. 5, American Mathematical Society, Providence, R.I., 1980. Translated from the Russian by R. P. Boas, J. M. Danskin, F. M. Goodspeed, J. Korevaar, A. L. Shields and H. P. Thielman. MR 589888
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 301-308
- MSC: Primary 34A20; Secondary 30D35
- DOI: https://doi.org/10.1090/S0002-9939-1987-0884470-4
- MathSciNet review: 884470