# Palindromic random trigonometric polynomials

@article{Conrey2008PalindromicRT,
title={Palindromic random trigonometric polynomials},
author={J. Brian Conrey and David W. Farmer and Ozlem Imamoglu},
journal={arXiv: Probability},
year={2008}
}
• Published 9 December 2008
• Mathematics
• arXiv: Probability
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…
1 Citations
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• 2020
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