Elementary recursive bounds for Hilbert 17th problem

HENRI LOMBARDI; DANIEL PERRUCCI; MARIE-FRANCOISE ROY

Singapur

Workshop; Polyhedra, Lattices, Algebra, and Moments; 2014

Institute for Mathematical Science - National University of Singapore

Hilbert 17th problem is to express a non-negative polynomial as a sum of squares of rational functions. The original proof by Artin is non-constructive and gives no information on the degree bounds. A more general problem is to give an identity which certifies the unrealizability of a system of polynomial equations and inequalities. The existence of such an identity is guaranteed by the Positivstellensatz. In this talk, we give a new constructive proof which provides elementary recursive bounds for the Positivstellensatz and Hilbert 17 problem, namely a tower of five levels of exponentials.