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

DOI:
https://doi.org/10.1090/S0002-9939-00-05779-8

Published electronically:
November 30, 2000

MathSciNet review:
1825904

Full-text PDF

Abstract | References | Similar Articles | Additional Information

A Bank-Laine function is an entire function satisfying at every zero of . 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:
https://doi.org/10.1090/S0002-9939-00-05779-8

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