Abstract
AbstractSuppose that E is a real entire function of finite order with zeros which are all real but neither bounded above nor bounded below, such that $$E'(z) = \pm 1$$
E
′
(
z
)
=
±
1
whenever $$E(z) = 0$$
E
(
z
)
=
0
. Then either E has an explicit representation in terms of trigonometric functions or the zeros of E have exponent of convergence at least 3. An example constructed via quasiconformal surgery demonstrates the sharpness of this result.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Analysis
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