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

 

Asymptotic behavior of roots of random polynomial equations


Authors: Efraim Shmerling and Kenneth J. Hochberg
Journal: Proc. Amer. Math. Soc. 130 (2002), 2761-2770
MSC (2000): Primary 60H25, 47B80, 34F05
Published electronically: March 13, 2002
MathSciNet review: 1900883
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Abstract: We derive several new results on the asymptotic behavior of the roots of random polynomial equations, including conditions under which the distributions of the zeros of certain random polynomials tend to the uniform distribution on the circumference of a circle centered at the origin. We also derive a probabilistic analog of the Cauchy-Hadamand theorem that enables us to obtain the radius of convergence of a random power series.


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Additional Information

Efraim Shmerling
Affiliation: Department of Mathematics, College of Judea and Samaria, 44837 Ariel, Israel

Kenneth J. Hochberg
Affiliation: Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel
Email: hochberg@macs.biu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06340-2
PII: S 0002-9939(02)06340-2
Keywords: Random polynomials
Received by editor(s): November 11, 2000
Received by editor(s) in revised form: March 23, 2001
Published electronically: March 13, 2002
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2002 American Mathematical Society