Acquistapace, FrancescaBroglia, FabrizioFernando Galván, José FranciscoRuiz Sancho, Jesús María2023-06-202023-06-202004-01-26https://hdl.handle.net/20.500.14352/50644We consider Hilbert’s 17 problem for global analytic functions in a modified form that involves infinite sums of squares. This reveals an essential connection between the solution of the problem and the computation of Pythagoras numbers of meromorphic functionsengjournal articlehttp://www.maths.manchester.ac.uk/raag/index.php?preprint=0083http://www.maths.manchester.ac.ukopen access512.7Hilbert 17th ProblemPythagoras numbersum of squaresbad setgerms at closed setsGeometria algebraica1201.01 Geometría Algebraica