On a problem of Erdős concerning the zeros of the derivatives of an entire function
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- by K. F. Barth and W. J. Schneider PDF
- Proc. Amer. Math. Soc. 32 (1972), 229-232 Request permission
Abstract:
Let $\{ {S_k}\}$ be any sequence of sets in the complex plane, each of which has no finite limit point. The authors prove, answering affirmatively a question posed by P. Erdös, that there exists a sequence $\{ {n_k}\}$ of positive integers and a transcendental entire function $f(z)$ such that ${f^{({n_k})}}(z) = 0$ if $z \in {S_k}$.References
- P. Erdös and A. Rényi, On the number of zeros of successive derivatives of analytic functions, Acta Math. Acad. Sci. Hungar. 7 (1956), 125–144 (English, with Russian summary). MR 80155, DOI 10.1007/BF02028197
- P. Erdös and A. Rényi, On the number of zeros of successive derivatives of entire functions of finite order, Acta Math. Acad. Sci. Hungar. 8 (1957), 223–225. MR 88555, DOI 10.1007/BF02025245
- W. K. Hayman, Research problems in function theory, The Athlone Press [University of London], London, 1967. MR 0217268
- J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 229-232
- MSC: Primary 30A66
- DOI: https://doi.org/10.1090/S0002-9939-1972-0293089-7
- MathSciNet review: 0293089