Vera Piquero, Carlos deParés Pàramo, Elena2020-02-212020-02-212019-06-20https://hdl.handle.net/2445/150977Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Carlos de Vera Piquero[en] The Hasse-Minkowski Theorem states that every quadratic form with rational coefficients has a non-trivial solution in the rational numbers if, and only if, it has a non-trivial solution in each completion of the rationals. We study all the completions of Q and present a proof of the theorem of Hasse-Minkowski using the Hilbert symbol and the theory of quadratic forms.50 p.application/pdfcatcc-by-nc-nd (c) Elena Parés Pàramo, 2019http://creativecommons.org/licenses/by-nc-nd/3.0/es/Formes quadràtiquesTreballs de fi de grauAnàlisi diofànticaPunts racionals (Geometria)Quadratic formsBachelor's thesesDiophantine analysisRational points (Geometryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess