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Euclidean quadratic forms and ADC forms: I

2012
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Acta Arithmetica
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A classical result of Aubry, Davenport and Cassels gives conditions for an integral quadratic form to integrally represent every integer that it rationally represents. We give a generalization which allows one to pass from rational to integral representations for suitable quadratic forms over a normed ring. The Cassels-Pfister theorem follows as another special case. This motivates a closer study of the classes of forms which satisfy the hypothesis of our theorem ("Euclidean forms") and its

doi:10.4064/aa154-2-3
fatcat:zfifatcpcbakjeend7sawomwb4