Acquistapace, FrancescaBroglia, FabrizioRuiz Sancho, Jesús María2023-06-202023-06-202007Bochnak, J., Risler, J.-J.: Le théorème des zéros pour les variétés analytiques réelles de dimension 2. Ann. Sci. Écol. Norm. Sup. Paris 8, 353–364 (1975) Campillo, A., Ruiz, J.M.: Some remarks on pythagorean real curve germs. J. Algebra 128,271–275 (1990) Choi, M.D., Dai, Z.D., Lam, T.Y., Reznick, B.: The Pythagoras number of some affine algebras and local algebras. J. Reine Angew. Math. 336, 45–82 (1982) Coen, S.: Sul rango dei fasci coerenti. Boll. UMI. 22, 373–383 (1967) Fernando, J.F., Quarez, R.: A remark on the Pythagoras number of algebroid curves. J. Algebra 274, 64–67 (2004) Fernando, J.F., Ruiz, J.M.: On the Pythagoras numbers of real analytic set germs. Bull. Soc.Math.France 133, 349–362 (2005) Fernando, J.F., Ruiz, J.M., Scheiderer, C.: Sums of squares in real rings. Trans. Am. Math.Soc. 356, 2663–2684 (2004) Jaworski, P.: Positive definite analytic functions and vector bundles. Bull. Acad. Polon. Sci. 30,501–506 (1982) Ortega, J.: On the Pythagoras number of a real irreducible algebroid curve. Math. Ann. 289,111–123 (1991) Quarez, R.: Pythagoras numbers of real algebroid curves and Gram matrices. J. Algebra 238,139–158 (2001) Ruiz, J.M.: On Hilbert’s 17th problem and real Nullstellensatz for global analytic functions.Math Z. 190, 447–459 (1985) Scheiderer, C.: Sums of squares of regular functions on real algebraic varieties. Trans. Am. Math.Soc. 352, 1039–1069 (1999) Scheiderer, C.: On sums of squares in local rings. J. Reine Angew. Math. 540, 205–227 (2001)0025-587410.1007/s00209-007-0107-6https://hdl.handle.net/20.500.14352/49899We show that the Pythagoras number of a real analytic curve is the supremum of the Pythagoras numbers of its singularities, or that supremum plus 1. This includes cases when the Pythagoras number is infinite.engjournal articlehttp://www.springerlink.com/content/v7545081u3w74649/fulltext.pdfhttp://www.springerlink.com/restricted access512.7511Pythagoras numberSum of squaresAnalytic curve GermGlobal analytic curveTeoría de númerosGeometria algebraica1205 Teoría de Números1201.01 Geometría Algebraica