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

 

On the expected number of zeros of a random harmonic polynomial


Authors: Wenbo V. Li and Ang Wei
Journal: Proc. Amer. Math. Soc. 137 (2009), 195-204
MSC (2000): Primary 34F05, 60G15; Secondary 26C10
Published electronically: August 7, 2008
MathSciNet review: 2439441
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Abstract: We study the distribution of complex zeros of Gaussian harmonic polynomials with independent complex coefficients. The expected number of zeros is evaluated by applying a formula of independent interest for the expected absolute value of quadratic forms of Gaussian random variables.


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Additional Information

Wenbo V. Li
Affiliation: Department of Mathematical Sciences, 517B Ewing Hall, University of Delaware, Newark, Delaware 19716
Email: wli@math.udel.edu

Ang Wei
Affiliation: Department of Mathematical Sciences, 308 Ewing Hall, University of Delaware, Newark, Delaware 19716
Email: wei@math.udel.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09555-5
PII: S 0002-9939(08)09555-5
Received by editor(s): December 14, 2007
Published electronically: August 7, 2008
Additional Notes: The first author was partially supported by an NSF grant DMS-0505805.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.