Palindromic random trigonometric polynomials
Authors:
J. Brian Conrey, David W. Farmer and Özlem Imamoglu
Journal:
Proc. Amer. Math. Soc. 137 (2009), 18351839
MSC (2000):
Primary 60G99; Secondary 42A05, 30C15
Published electronically:
December 15, 2008
MathSciNet review:
2470844
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: We show that if a real trigonometric polynomial has few real roots, then the trigonometric polynomial obtained by writing the coefficients in reverse order must have many real roots. This is used to show that a class of random trigonometric polynomials has, on average, many real roots. In the case that the coefficients of a real trigonometric polynomial are independently and identically distributed, but with no other assumptions on the distribution, the expected fraction of real zeros is at least onehalf. This result is best possible.
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Additional Information
J. Brian Conrey
Affiliation:
Department of Mathematics, American Institute of Mathematics, 360 Portage Avenue, Palo Alto, California 94306
Email:
conrey@aimath.org
David W. Farmer
Affiliation:
Department of Mathematics, American Institute of Mathematics, 360 Portage Avenue, Palo Alto, California 94306
Email:
farmer@aimath.org
Özlem Imamoglu
Affiliation:
Department of Mathematics, Eidgen Technische Hochschule, CH8092 Zurich, Switzerland
Email:
ozlem@math.ethz.ch
DOI:
http://dx.doi.org/10.1090/S0002993908097761
PII:
S 00029939(08)097761
Received by editor(s):
August 12, 2008
Published electronically:
December 15, 2008
Additional Notes:
The research of the first two authors was supported by the American Institute of Mathematics and the National Science Foundation
Communicated by:
Richard C. Bradley
Article copyright:
© Copyright 2008
American Mathematical Society
