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...

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Detalles Bibliográficos
Autores: Fernando Galván, José Francisco, Ruiz Sancho, Jesús María, Scheiderer, Claus
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
Descripción
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.