An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem

An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem (pdf)
preprint 2014. arXiv 1404.2338
with Daniel Perrucci and Marie-Françoise Roy.

Abstract :

We prove elementary recursive bounds in the degrees for Positivstellensatz and Hilbert 17-th problem, which is the expression of a nonnegative polynomial as a sum of squares of rational functions. We obtain a tower of five exponentials.