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

 

The Lu Qi-Keng conjecture fails
for strongly convex algebraic complete
Reinhardt domains in ${\mathbb{C}}^{n}$ $(n \geq 3)$


Author: Nguyên Viêt Anh
Journal: Proc. Amer. Math. Soc. 128 (2000), 1729-1732
MSC (1991): Primary 32H10
Published electronically: October 29, 1999
MathSciNet review: 1653405
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Abstract: In this note, we give an example of a strongly convex algebraic complete Reinhardt domain which is not Lu Qi-Keng in ${\mathbb{C}}^{n}$ for any $n \geq 3.$


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Additional Information

Nguyên Viêt Anh
Affiliation: Université de Provence, LATP U.M.R C.N.R.S 6632, C.M.I, 39, rue Joliot-Curie, 13453 Marseille Cedex 13, France
Email: vietanh@gyptis.univ-mrs.fr.

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05228-4
PII: S 0002-9939(99)05228-4
Keywords: Lu Qi-Keng conjecture, Bergman kernel
Received by editor(s): July 14, 1998
Published electronically: October 29, 1999
Communicated by: Steven R. Bell
Article copyright: © Copyright 2000 American Mathematical Society