RT Journal Article T1 On the Pythagoras numbers of real analytic curves. A1 Acquistapace, Francesca A1 Broglia, Fabrizio A1 Ruiz Sancho, Jesús María AB We 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. PB Springer SN 0025-5874 YR 2007 FD 2007 LK https://hdl.handle.net/20.500.14352/49899 UL https://hdl.handle.net/20.500.14352/49899 LA eng NO Bochnak, 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) NO GNSAGA NO INdAM NO MIUR NO GEOR NO UCM DS Docta Complutense RD 3 may 2024