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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bank-Laine functions with sparse zeros


Author: J. K. Langley
Journal: Proc. Amer. Math. Soc. 129 (2001), 1969-1978
MSC (2000): Primary 30D35; Secondary 34M05, 34M10
Published electronically: November 30, 2000
MathSciNet review: 1825904
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Abstract:

A Bank-Laine function is an entire function $E$ satisfying $E'(z) = \pm 1$ at every zero of $E$. We construct a Bank-Laine function of finite order with arbitrarily sparse zero-sequence. On the other hand, we show that a real sequence of at most order 1, convergence class, cannot be the zero-sequence of a Bank-Laine function of finite order.


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Additional Information

J. K. Langley
Affiliation: School of Mathematical Sciences, University of Nottingham, NG7 2RD United Kingdom
Email: jkl@maths.nott.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05779-8
PII: S 0002-9939(00)05779-8
Received by editor(s): July 6, 1999
Received by editor(s) in revised form: October 13, 1999
Published electronically: November 30, 2000
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society