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Title: on the zeros of ∑ aiexpgi
Authors: Ng, Tuen-Wai
Yang, Chung-Chun
Keywords: Zero set
Entire function
Borel theorem
Upper half-plane
Nevanlinna theory
Issue Date: 1997
Citation: Proceedings of the Japan Academy. Series A, Mathematical sciences, v. 73, 1997, p. 137-139
Abstract: We consider entire functions of the form f = ∑ aiegi, where ai(≠0), gi are entire functions and the orders of all ai are less than one. If all the zeros of f are real, then f = eg ∑ aiehi where hi are linear functions. Using this result, we can prove that f = aieg if all zeros of f are positive, which also generalizes a result obtained by A. Eremenko and L. A. Rubel.
Rights: © The Japan Academy. Reproduced with permission.
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