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A note on the zero-sequences of solutions of 
Author(s):
Andreas
Sauer
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1143-1147.
MSC (1991):
Primary 34A20;
Secondary 30D20
MathSciNet review:
1377005
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Abstract:
We give a sufficient condition for complex sequences to be zero-sequences of solutions of  where  is transcendental entire and of finite order.
References:
- [B]
- S. Bank, A note on the zero-sequences of solutions of linear differential equations, Resultate Math. 13 (1988), 1-11. MR 89b:34009
- [BL]
- S. Bank, I. Laine, On the oscillation theory of
 where  is entire, Trans. Amer. Math. Soc. 273 (1982), 351-363. MR 83k:34009 - [BS]
- H. Behnke, F. Sommer, Theorie der analytischen Funktionen einer komplexen Veränderlichen, Springer, Berlin-Göttingen-Heidelberg-New York, 1962. MR 26:5137
- [HC]
- A. Hurwitz, R. Courant, Funktionentheorie, Springer, Berlin-Göttingen-Heidelberg-New York, 1964. MR 30:3959
- [L]
- I. Laine, Nevanlinna Theory and Complex Differential Equations, de Gruyter, Berlin - New York, 1993. MR 94d:34008
- [N]
- R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929. MR 54:5468
- [S]
- L. C. Shen, Construction of a differential equation
 with solutions having the prescribed zeros, Proc. Amer. Math. Soc. 95 (1985), 544-546.MR 87b:34005
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Additional Information:
Andreas
Sauer
Affiliation:
Gerhard Mercator Universität, Fachbereich 11 Mathematik, Lotharstrasse 65, D-47057 Duisberg, Federal Republic of Germany
Email:
sauer@math.uni-duisberg.de
DOI:
10.1090/S0002-9939-97-03819-7
PII:
S 0002-9939(97)03819-7
Received by editor(s):
October 11, 1995
Additional Notes:
This research was done during a visit at the University of Joensuu, Finland, financed by the DFG (Deutsche Forschungsgemeinschaft).
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1997,
American Mathematical Society
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