@inproceedings{a8435b08a0c6453eb8e3efe796a94609,

title = "A quantitative P{\'o}lya's theorem with corner zeros",

abstract = "P{\'o}lya's Theorem says that if p is a homogeneous polynomial in n variables which is positive on the standard n-simplex, and F is the sum of the variables, then for a sufficiently large exponent N, FN * p has positive coefficients. P{\'o}lya's Theorem has had many applications in both pure and applied mathematics; for example it provides a certificate for the positivity of p on the simplex. The authors have previously given an explicit bound on N, determined by the data of p; namely, the degree, the size of the coefficients and the minimum value of p on the simplex. In this paper, we extend this quantitative P{\'o}lya's Theorem to non-negative polynomials which are allowed to have simple zeros at the corners of the simplex.",

keywords = "Positive polynomials, P{\'o}lya's theorem, Sums of squares",

author = "Victoria Powers and Bruce Reznick",

year = "2006",

doi = "10.1145/1145768.1145815",

language = "English (US)",

isbn = "1595932763",

series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",

publisher = "Association for Computing Machinery",

pages = "285--289",

booktitle = "Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, ISSAC 2006",

address = "United States",

note = "International Symposium on Symbolic and Algebraic Computation, ISSAC 2006 ; Conference date: 09-07-2006 Through 12-07-2006",

}