Pólya’s Theorem with Zeros

Authors

Mari Castle, Kennesaw State UniversityFollow
Victoria Powers, Emory University
Bruce Reznick, University of Illinois at Urbana-Champaign

Department

Mathematics

Document Type

Article

Publication Date

9-2011

Abstract

Let be the real polynomial ring in variables. Pólya’s Theorem says that if a homogeneous polynomial is positive on the standard -simplex , then for sufficiently large all the coefficients of are positive. We give a complete characterization of forms, possibly with zeros on , for which there exists so that all coefficients of have only nonnegative coefficients, along with a bound on the needed.

Journal Title

Journal of Symbolic Computation

Journal ISSN

0747-7171

Volume

46

Issue

9

First Page

1039

Last Page

1048

Digital Object Identifier (DOI)

10.1016/j.jsc.2011.05.006