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Bank-Laine Functions with Real Zeros
Computational Methods and Function Theory ( IF 2.1 ) Pub Date : 2020-09-24 , DOI: 10.1007/s40315-020-00342-9
J. K. Langley

Suppose 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 \(E'(z) = \pm 1\) whenever \(E(z) = 0\). 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.



中文翻译:

具有实零点的Bank-Laine函数

假设E是一个有限阶的实整函数,且所有零均为实数,但既无上界也无下界,因此\(E'(z)= \ pm 1 \)每当\(E(z)= 0 \ )。然后,E具有三角函数的明确表示形式,或者E的零具有至少3的收敛指数。通过准保形手术构造的示例证明了该结果的鲜明性。

更新日期:2020-09-24
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