The Genus of a Quadratic Form
نویسنده
چکیده
Our basic problem is to answer the question : when are two quadratic forms equivalent by a rational or integral change of basis? We shall temporarily suppose that all our forms are non-degenerate (i.e., have non-zero determinant), although degenerate forms really give no trouble, The answer in the rational case is given by the celebrated HasseMinkowski theorem, which is usually stated in the form:
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