Algebra Seminar

Marie-Franoise Roy, Universite de Rennes (France)

“Recursive bound for Hilbert 17-th problem”

Artin’s beautiful proof of Hilbert 17 th problem is higly non constructive. Constructive proofs obtained by Kreisel and others provided only primitive recursive degree bounds. We prove elementary recursive bounds in the degree for Hilbert 17-th problem, which is the ex- pression of a nonnegative polynomial as a sum of squares of rational functions. We obtain a tower of five exponentials. The method to obtaind a precise bound in terms of the degree of the polynomial and their number of variables will be presented. (Joint work with Henri Lombardi, Daniel Perrucci.)

MC 5501

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