Euclidean Quadratic Forms and ADC Forms I

Pete L. Clark

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Euclidean Quadratic Forms and ADC Forms I

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arxiv 1208.0974 v1 pith:QPMVRTH3 submitted 2012-08-05 math.NT

Euclidean Quadratic Forms and ADC Forms I

Pete L. Clark This is my paper

classification math.NT

keywords formseuclideanquadraticclassicaldomainformintegralresults

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Motivated by classical results of Aubry, Davenport and Cassels, we define the notion of a Euclidean quadratic form over a normed integral domain and an ADC form over an integral domain. The aforementioned classical results generalize to: Euclidean forms are ADC forms. We then initiate the study and classification of these two classes of quadratic forms, especially over discrete valuation rings and Hasse domains.

Euclidean Quadratic Forms and ADC Forms I

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