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On the Pythagoras numbers of real analytic curves |
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| Authors: | Francesca Acquistapace Fabrizio Broglia José F Fernando Jesús M Ruiz |
| Institution: | (1) Dipartimento di Matematica, Università degli Studi di Pisa, Via Filippo Buonarroti, 2, 56127 Pisa, Italy;(2) Departamento de álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain;(3) Departamento de Geometrí a y Topología, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain |
| Abstract: | 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. |
| Keywords: | Pythagoras number Sum of squares Analytic curve germ Global analytic curve |
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