Sums of squares of linear forms: the quaternions approach
Let A = k[y] be the polynomial ring in one single variable y over a field k. We discuss the number of squares needed to represent sums of squares of linear forms with coefficients in the ring A. We use quaternions to obtain bounds when the Pythagoras number of A is ≤ 4. This provides bounds for the...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2006 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/50666 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/50666 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.7 Pythagoras number Pfister bound quaternions Geometria algebraica 1201.01 Geometría Algebraica |
| Sumario: | Let A = k[y] be the polynomial ring in one single variable y over a field k. We discuss the number of squares needed to represent sums of squares of linear forms with coefficients in the ring A. We use quaternions to obtain bounds when the Pythagoras number of A is ≤ 4. This provides bounds for the Pythagoras number of algebraic curves and algebroid surfaces over k. |
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